NMZ Nuveen Municipal High Income Opportunity Fund

Filed Pursuant to Rule 424(b)(3)

File No. 333-253965

NUVEEN MUNICIPAL HIGH INCOME OPPORTUNITY FUND (NYSE: NMZ)

(THE “FUND”)

SUPPLEMENT DATED MAY 31, 2023

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

DATED MARCH 5, 2021, 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 Stephen J. Candido, 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