EX-99.906CERT

EXHIBIT 13 (b)

RULE 30a-2(b) CERTIFICATIONS

In connection with the Report of Cohen & Steers Institutional Realty Shares, Inc. (the “Company”) on Form N-CSR as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Adam M. Derechin, Principal Executive Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Adam M. Derechin

Adam M. Derechin

Principal Executive Officer

(President and Chief Executive Officer)

Date: August 27, 2021

EXHIBIT 13 (b)

RULE 30a-2(b) CERTIFICATIONS

In connection with the Report of Cohen & Steers Institutional Realty Shares, Inc. (the “Company”) on Form N-CSR as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, James Giallanza, Principal Financial Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as applicable; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ James Giallanza

James Giallanza

Principal Financial Officer

(Chief Financial Officer)

Date: August 27, 2021