Exhibit 99.1

June 15, 2018

Board of Directors

InfuSystem Holdings, Inc.

31700 Research Park Drive

Madison Heights, Michigan 48071

Ladies and Gentlemen:

As you know, Meson Capital Partners LLC (“Meson”) through its affiliated entities owns approximately 9.5% of the outstanding common stock of InfuSystem Holdings, Inc. (the “Company”). In addition, Ryan Morris, the Managing Member and sole owner of Meson, previously served as a director of the Company. Meson previously advised the Board, and disclosed publicly in its Schedule 13D filing, that it may, among other things, consider, explore and/or develop plans and/or make proposals with respect to potential strategic transactions involving the Company.

Subsequent to filing its Schedule 13D, Meson reached out to Argonne Capital Group, a closely-held private investment firm (“Argonne”), to assist in assessing and moving forward with potential strategic transactions involving the Company. We have collectively been reviewing the Company’s strategy and financial position. We believe the Company can be more entrepreneurial if it is private and thereby be in a better position to thrive. Accordingly, after careful consideration and analysis, we believe the most favorable alternative for all stakeholders is a public-to-private transaction that we propose herein with the financial support of Argonne, on behalf of itself and/or with financing provided by other financial institutions identified by Argonne.

We believe that the Company and its employees would benefit greatly in the long run from private ownership of the Company, which would enable the Company to execute a long-term value creation strategy. Alongside Meson’s equity roll-over contribution and Argonne and other financial institutions providing financing for the transaction, we believe we will be able to obtain substantial capital resources for the benefit of the Company, in the form of both debt and equity to help fund future acquisitions and an aggressive organic growth strategy.

Proposal and Valuation

We have devoted a substantial amount of time and resources preparing this proposal that delivers fair and compelling value to Company shareholders and provides substantial assurance of closing on a timely basis.

The purchase price for the Company’s shares would be $3.75 per share. We believe this offer presents an excellent opportunity for Company shareholders to realize an attractive, all-cash premium for their shares at a favorable valuation in a very challenging operating environment. The proposal creates immediate liquidity for Company shareholders, an opportunity not otherwise available to them given the market capitalization and trading characteristics of the Company’s stock. This valuation represents (i) a 56% premium over the unaffected closing price on March 20, 2018, the day immediately preceding the date Meson filed its Schedule 13D disclosing its potential interest in engaging in strategic transactions with the Company; (ii) a 29% premium over the unaffected closing price on April 25, 2018, when Meson announced that it intended to continue a dialogue with Company management and the Board about a broad range of strategic and operational matters and Mr. Morris delivered a letter to the Company nominating six highly-qualified director candidates; and (iii) a premium to the stock’s 52-week high.

We believe that it would be in the best interests of the Company and its shareholders to pursue a transaction at $3.75 per share.

Financing

As indicated above, we expect to finance the transaction with a combination of debt and equity. Meson contemplates contributing its existing equity ownership of the Company. While we may seek additional financing sources, Meson has currently elected to work with Argonne a proven financial sponsor that has successfully deployed over $780 million of equity since inception in over 20 private equity transactions. Meson and Argonne can provide all the equity anticipated to be necessary to consummate the transaction. Further, based upon our preliminary conversations with several leading healthcare lenders, we are highly confident that we can obtain any necessary debt financial commitments needed to complete the proposed transaction.

Timing and Advisors

Given our extensive knowledge of the Company, we are well positioned to negotiate and complete the transaction in an expedited manner and to promptly enter into discussions so that we can negotiate a merger agreement acceptable to all parties. In furtherance of this, we request that the Board delay the 2018 Annual Meeting of Stockholders, so the Board may devote its full attention to considering our offer. We are prepared to sign a standard NDA and conduct diligence promptly. We are confident that a transaction would receive all necessary regulatory approvals, including antitrust clearances, and as discussed herein we fully expect to have the necessary financing to close the transaction. To facilitate a transaction, Meson has engaged Olshan Frome Wolosky LLP as its legal counsel. If this proposal is accepted, Argonne will engage King & Spalding or another firm of its choosing as its legal counsel. We are ready to negotiate a definitive merger agreement which would contain customary terms and conditions for transactions of this type. Our respective representatives are available to meet with the CEO and Board of Directors to discuss this proposal at your earliest convenience.

Conditions and Due Diligence

Any transaction would be subject to: (a) completion of due diligence, including financial, legal, accounting and tax diligence, with results satisfactory to us in our sole discretion; (b) receipt of financing commitments with respect to the financing necessary to complete this transaction; (c) negotiation of a satisfactory acquisition agreement with customary terms and conditions; and (d) reaching agreements with the management of the Company with respect to their ongoing roles as managers of the Company. We are prepared to commence work immediately to satisfy these conditions. We are highly confident that the conditions can be satisfied expeditiously.

No Binding Commitment

This letter does not constitute a binding commitment or obligation of the undersigned and the undersigned may terminate discussions regarding this proposal or a transaction at any time and for any reason (or no reason). No commitment (including any obligation to negotiate) shall arise with respect to this acquisition proposal or a transaction unless and until such time as definitive documentation that is satisfactory to the undersigned and approved by the board of directors of the Company is executed and delivered, and then will be on the terms provided in such documentation.

Introduction to Argonne Capital Group

Argonne is a closely-held private investment firm founded in 2003 and based in Atlanta, Georgia. Argonne seeks to acquire and grow companies that will benefit from the firm’s capital resources and operational expertise and capabilities. Argonne pursues partnerships with strong management teams to develop quality companies and help them achieve improved scale by new unit growth, operational improvements and industry consolidation. To date, Argonne has completed 21 transactions and currently has invested over $780 million of equity capital since inception. Today, Argonne’s portfolio of companies employs over 32,000 people and generates $1.5 billion in annual system sales.

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While we appreciate and respect the Board’s need to conduct an appropriate process in evaluating our proposal, time is of the essence and your prompt consideration to this proposal is requested. As noted above, to facilitate the Company’s timely consideration of our offer, we request the Board delay the 2018 Annual Meeting of Stockholders.

Meson is pleased that the $3.75 per share offer is being made with Argonne, a leading private investment firm. We hope to work with you on a negotiated basis to complete this transaction successfully, and are prepared to deliver a draft merger agreement, subject to our diligence process. We suggest that we enter into a Non-Disclosure Agreement with you so that we can begin due diligence and discussions with your financial and legal advisors at your earliest convenience to work toward the goal of announcing a draft merger agreement in the very near future. Due to the importance of these discussions and the value represented by our proposal, we expect the Company’s Board to engage in a full review of our proposal. We would be happy to make our team available to meet with the Board at your earliest convenience. To the extent we fail to hear a favorable response from the Board to our proposal by June 19, 2018, we intend to evaluate all of our options as stockholders of the Company and take appropriate action with respect to our investment.

Sincerely,