Exhibit 99.906CERT

Certification Pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002; provided by the Chief Executive Officer and Chief Financial Officer, based on each such officer’s knowledge and belief.

The undersigned officers of Nuveen AMT-Free Quality Municipal Income Fund (the “Fund”) certify that, to the best of each such officer’s knowledge and belief:

1. The Form N-CSR of the Fund for the period ended October 31, 2021 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

Date: January 6, 2022

/s/ David J. Lamb

David J. Lamb

Chief Administrative Officer

(principal executive officer)

/s/ E. Scott Wickerham

E. Scott Wickerham

Vice President, Controller

(principal financial officer)