NBB Nuveen Taxable Municipal Income Fund

Filed Pursuant to Rule 424(b)(3)

File No. 333-248493

NUVEEN TAXABLE MUNICIPAL INCOME FUND (NYSE: NBB)

(THE “FUND”)

SUPPLEMENT DATED MAY 31, 2023

TO THE FUND’S PROSPECTUS AND STATEMENT OF ADDITIONAL INFORMATION (“SAI”)

DATED JANUARY 21, 2021, EACH AS SUPPLEMENTED

As previously announced on April 10, 2023, John V. Miller, CFA, effective today is no longer a portfolio manager of the Fund. Daniel J. Close, CFA, and Kristen DeJong, CFA, continue to serve as portfolio managers of the Fund. Based on the foregoing, all references and information relating to Mr. Miller are removed from the Fund’s Prospectus and SAI, and any supplements thereto.

PLEASE KEEP THIS WITH YOUR FUND’S

PROSPECTUS AND SAI FOR FUTURE REFERENCE