Nuveen Municipal High Income Opportunity Fund (NMZ) 424B3 Prospectus supplement

Filed Pursuant to Rule 424(b)(3)

File No. 333-253965

NUVEEN MUNICIPAL HIGH INCOME OPPORTUNITY FUND

(NYSE: NMZ)

(THE “FUND”)

SUPPLEMENT DATED JULY 14, 2023

TOTHE FUND’S PROSPECTUSAND STATEMENTOF ADDITIONAL INFORMATION (“SAI”)

DATED MARCH 5, 2021,EACHAS SUPPLEMENTED,ANDEACH PROSPECTUS SUPPLEMENT

The Board of Directors of the Fund has approved a change to the Fund’s maturity policy.

Effective immediately, (1) the first sentence of the tenth paragraph in the section of the Fund’s Prospectus Summary, and each Prospectus Supplement, entitled “Investment Objectives and Policies”; (2) the second sentence under the eighth paragraph in the section of the Fund’s Prospectus entitled “Municipal Securities”; and (3) the first and third sentences of the thirteenth paragraph under “Investment Policies” in the SAI are deleted in their entirety and replaced with the following:

Under normal market conditions, the Fund will generally maintain an investment portfolio with an overall weighted average maturity of greater than 10 years.

PLEASE KEEP THIS WITH YOUR

FUND’S PROSPECTUS AND SAI FOR FUTURE REFERENCE