Filed Pursuant to Rule 424(b)(3)
Registration No. 333-277778

Nuveen Municipal High Income Opportunity Fund (NYSE: NMZ)

(the “Fund”)

Supplement Dated May 9, 2025

to the Fund’s Currently Effective Prospectus

Effective May 9, 2025, Steven Hlavin has been added to the portfolio management team of the Fund. The following information is hereby added under the heading “Management of the Fund – Investment Adviser, Sub-Adviser and Portfolio Manager—Portfolio Manager” of the Prospectus:

“Steven Hlavin is a Managing Director and Portfolio Manager at Nuveen. As a member of the High Yield Municipal Portfolio Management Team, he is responsible for supporting all High Yield Municipal strategies and is specifically responsible for managing the Enhanced High Yield Municipal Bond, High Yield Municipal Opportunities LP, Municipal Opportunities and Short Duration High Yield Municipal Bond Strategies. He oversees a number of state-specific, tax-exempt portfolios including the Kansas Municipal Bond, Louisiana Municipal Bond and Wisconsin Municipal Bond Strategies. He is also responsible for the tender option bond/inverse floating rate program used by some of the firm’s closed-end and open-end funds. Steven began his career with Nuveen in 2003, also working as a senior analyst responsible for risk management and performance measurement processes, developing yield curve strategies and portfolio optimization techniques. He received his B.A. in Finance and Accounting and an M.B.A. in Finance from Miami University.”

PLEASE KEEP THIS WITH YOUR

FUND’S PROSPECTUS FOR FUTURE REFERENCE

EGN-NMZP-0525P

Nuveen Municipal High Income Opportunity Fund (NYSE: NMZ)

(the “Fund”)

Supplement Dated May 9, 2025

to the Fund’s Currently Effective

Statement of Additional Information (“SAI”)

Effective May 9, 2025, Steven Hlavin has been added to the portfolio management team of the Fund. The following information is hereby added under the heading “Investment Adviser, Sub-Adviser and Portfolio Managers—Portfolio Managers—Portfolio Management” of the SAI:

“Steven Hlavin is a Managing Director and Portfolio Manager at Nuveen. As a member of the High Yield Municipal Portfolio Management Team, he is responsible for supporting all High Yield Municipal strategies and is specifically responsible for managing the Enhanced High Yield Municipal Bond, High Yield Municipal Opportunities LP, Municipal Opportunities and Short Duration High Yield Municipal Bond Strategies. He oversees a number of state-specific, tax-exempt portfolios including the Kansas Municipal Bond, Louisiana Municipal Bond and Wisconsin Municipal Bond Strategies. He is also responsible for the tender option bond/inverse floating rate program used by some of the firm’s closed-end and open-end funds. Steven began his career with Nuveen in 2003, also working as a senior analyst responsible for risk management and performance measurement processes, developing yield curve strategies and portfolio optimization techniques. He received his B.A. in Finance and Accounting and an M.B.A. in Finance from Miami University.”

The following information is hereby added under the heading “Investment Adviser, Sub-Adviser and Portfolio Managers—Portfolio Managers—Other Accounts Managed” of the SAI:

¹ Began serving as a portfolio manager of the Fund on May 9, 2025. Information provided is as of March 31, 2025.

The following information is hereby added under the heading “Investment Adviser, Sub-Adviser and Portfolio Managers—Portfolio Managers—Fund shares owned by the Portfolio Manager” of the SAI:

¹ Began serving as a portfolio manager of the Fund on May 9, 2025. Information provided is as of March 31, 2025.

PLEASE KEEP THIS WITH YOUR

FUND’S SAI FOR FUTURE REFERENCE

EGN-NMZS-0525P