Definitive Materials Filed by Investment Companies. (497)

NUVEEN AMT-FREE MUNICIPAL VALUE FUND

(NYSE: NUW)

SUPPLEMENT DATED MAY 21, 2020

TO THE PROSPECTUS DATED SEPTEMBER 3, 2019,

AS AMENDED ON MARCH 24, 2020

In accordance with an undertaking required by the U.S. Securities and Exchange Commission, the Nuveen AMT-Free Municipal Value Fund (the “Fund”) temporarily suspended its “at the market” offering (the “Offering”) as of the close of business on March 19, 2020 because of a greater than 10% decline in net asset value per common share of beneficial interest (the “Shares”) from the effective date of the Fund’s prospectus. The net asset value of the Fund as of March 19, 2020 was $15.32, representing a decline of 10.7% from its net asset value of $17.15 as of September 3, 2019.

The net asset value at the close of business on May 19, 2020 was $16.13, representing a decline of approximately 5.9% from the September 3, 2019 net asset value. The last reported market price per Share on May 19, 2020 on the New York Stock Exchange was $14.76.

The decline in the Fund’s net asset value is principally the result of market value decreases in the Fund’s investments, particularly in light of general market and government reactions to the spread of COVID-19 in the United States. The Offering will recommence on or about the day of this supplement.

PLEASE KEEP THIS WITH YOUR FUND’S

PROSPECTUS AND STATEMENT OF ADDITIONAL INFORMATION

FOR FUTURE REFERENCE

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