NMZ Nuveen Municipal High Income Opportunity Fund

Nuveen Municipal High Income Opportunity Fund (NYSE: NMZ)

(the “Fund”)

Supplement Dated May 20, 2024

to the Fund’s Currently Effective Prospectus

Effective May 1, 2024, the information appearing under the heading “Management of the Fund – Investment Management and Sub-Advisory Agreements – Complex-Level Fee” of the Prospectus is hereby deleted and replaced with the following:

Complex-Level Fee. The overall complex-level fee, payable monthly, begins at a maximum rate of 0.1600% of the Fund’s average daily managed assets, with breakpoints for eligible complex-level assets above $124.3 billion. Therefore, the maximum management fee rate for the Fund is the Fund-level fee plus 0.1600%. The current overall complex-level fee schedule is as follows:

^* See “Investment Adviser, Sub-Adviser and Portfolio Managers” in the SAI for more detailed information about the complex-level fee and eligible complex-level assets.

PLEASE KEEP THIS WITH YOUR

FUND’S PROSPECTUS FOR FUTURE REFERENCE

EGN-NMZP-0524P

Nuveen Municipal High Income Opportunity Fund (NYSE: NMZ)

(the “Fund”)

Supplement Dated May 20, 2024

to the Fund’s Currently Effective

Statement of Additional Information (“SAI”)

Effective May 1, 2024, the information appearing under the heading “Investment Adviser, Sub-Adviser and Portfolio Managers – Complex-Level Fee” of the SAI is hereby deleted and replaced with the following:

Complex-Level Fee. The overall complex-level fee, payable monthly, begins at a maximum rate of 0.1600% of the Fund’s average daily managed assets, with breakpoints for eligible complex-level assets above $124.3 billion. Therefore, the maximum management fee rate for the Fund is the Fund-level fee plus 0.1600%. The current overall complex-level fee schedule is as follows:

^* The complex-level fee is calculated based upon the aggregate daily “eligible assets” of all Nuveen-branded closed-end funds and Nuveen Mutual Funds. Except as described below, eligible assets include the net assets of all Nuveen-branded closed-end funds and Nuveen Mutual Funds organized in the United States. Eligible assets do not include the net assets of: Nuveen fund-of-funds, Nuveen money market funds, Nuveen index funds, Nuveen Large Cap Responsible Equity Fund or Nuveen Life Large Cap Responsible Equity Fund. In addition, eligible assets include a fixed percentage of the aggregate net assets of the active equity and fixed income Nuveen Mutual Funds advised by Teachers Advisors, LLC (“TAL”) (except those identified above). Eligible assets will include all of the aggregate net assets of TAL-advised active equity and fixed income Nuveen Mutual Funds (except those identified above) on May 1, 2033. Eligible assets include closed-end fund assets managed by Nuveen Fund Advisors that are attributable to financial leverage. For these purposes, financial leverage includes the closed-end funds’ use of preferred stock and borrowings and certain investments in the residual interest certificates (also called inverse floating rate securities) in tender option bond (TOB) trusts, including the portion of assets held by a TOB trust that has been effectively financed by the trust’s issuance of floating rate securities, subject to an agreement by Nuveen Fund Advisors as to certain funds to limit the amount of such assets for determining eligible assets in certain circumstances.

PLEASE KEEP THIS WITH YOUR

FUND’S SAI FOR FUTURE REFERENCE

EGN-NMZS-0524P

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