Exhibit (a)(5)(i)

Cryo-Cell Commences Tender Offer to Purchase its Common Stock

Up to 750,000 Shares at $3.25 per Share

Oldsmar, FL—June 30, 2015—Cryo-Cell International, Inc. (OTCBB: CCEL), the world’s first private cord blood bank to separate and store stem cells in 1992, announced today that it has commenced a partial tender offer to purchase up to 750,000 shares of its common stock, at a price of $3.25 per share.

The maximum number of shares proposed to be purchased in the tender offer represents approximately 7.76% of Cryo-Cell’s currently outstanding common shares (including shares of unvested restricted stock). On June 29, 2015, the last trading day prior to the commencement of the tender offer, the last sale price of Cryo-Cell’s shares reported on the OTCBB was $2.29 per share.

The tender offer will expire on July 28, 2015 at midnight (one minute after 11:59 p.m.), New York time, unless extended. Tenders of shares of Cryo-Cell’s common stock must be made on or prior to the expiration of the tender offer and may be withdrawn at any time on or prior to the expiration of the tender offer. Only shares properly tendered and not properly withdrawn pursuant to the tender offer will be purchased. The tender offer will be financed entirely with cash on hand. Cryo-Cell reserves the right, in its sole discretion, to purchase in the tender offer, subject to applicable law, an additional number of shares not to exceed 2% of the outstanding shares without amending or extending the tender offer.

This press release is for informational purposes only and does not constitute an offer to purchase or the solicitation of an offer to sell shares of Cryo-Cell’s common stock. The tender offer is being made pursuant to the Offer to Purchase, Letter of Transmittal and related materials that Cryo-Cell is sending to its stockholders and has filed with the Securities and Exchange Commission. The tender offer materials contain important information that should be read carefully before any decision is made with respect to the tender offer. Those materials (and all other offer documents filed with the SEC) will be available at no charge on the SEC’s website at www.sec.gov or by contacting Laurel Hill Advisory Group, LLC, the Information Agent for the tender offer, at 1-(888) 742-1305. Questions concerning the tender offer should be directed to the Information Agent at 1-888-742-1305. Continental Stock Transfer and Trust Company is the Depositary for the tender offer.

None of Cryo-Cell, its board of directors, the Information Agent or the Depositary is making any recommendation to stockholders as to whether to tender or refrain from tendering any shares. Stockholders and investors should read carefully the Offer to Purchase, Letter of Transmittal and related materials, should consult with their own financial and tax advisors, and should make their own decisions about whether to tender shares, and, if so, how many shares to tender.

About Cryo-Cell

Founded in 1989, Cryo-Cell is the world’s first private cord blood bank. More than 500,000 parents from 87 countries trust Cryo-Cell to preserve their family members’ stem cells. Cryo-Cell’s mission is to provide clients with state-of-the-art stem cell cryopreservation services and support the advancement of regenerative medicine. Cryo-Cell operates in a facility that is FDA registered, cGMP-/cGTP-compliant and is licensed in all states requiring licensure. Besides being AABB accredited as a cord blood facility, Cryo-Cell is also the first U.S. (for private use only) cord blood bank to receive FACT accreditation for adhering to the most stringent cord blood quality standards set by any internationally recognized, independent accrediting organization. In addition, Cryo-Cell is ISO 9001:2008 certified by BSI, an internationally recognized, quality assessment organization.

This press release contains forward-looking statements that are other than statements of historical fact, including those regarding the expected timing of the tender offer described in this press release. These statements are based on our current plans and expectations and involve risks and uncertainties that could cause actual future events or results to be different from those described in or implied by such forward-looking statements, including the tender offer being subject to certain conditions set forth in the Offer to Purchase and changes in facts and circumstances and other uncertainties concerning the completion of the tender offer. Statements in this release should be evaluated in light of these factors. These risk factors and other important factors that could affect our business and financial results are discussed in our periodic reports and filings with the Securities and Exchange Commission, which are available at www.sec.gov. Except as required by applicable law or regulation, Cryo-Cell undertakes no duty to update or revise any forward-looking statements. Notwithstanding anything in this press release, the safe harbor protections of the Private Securities Litigation Reform Act of 1995 do not apply to statements made in connection with a tender offer.

2