Supplemental Prospectus (Form 424B3)

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

Nuveen Municipal high income opportunity Fund (NYSE: nmz)

(the "Fund")

Supplement Dated April 24, 2026

to the Fund's Prospectus Supplement Dated April 4, 2024

(the "Prospectus Supplement")

Capitalized terms used in this supplement, unless otherwise defined in this supplement, have the meanings assigned to them in the Prospectus Supplement.

The Fund has previously entered into a distribution agreement with Nuveen Securities, LLC ("Nuveen Securities") pursuant to which the Fund may from time-to-time issue and sell its Common Shares through Nuveen Securities to certain broker-dealers that have entered into selected dealer agreements with Nuveen Securities. Nuveen Securities has entered into a selected dealer agreement with Virtu Americas LLC ("Virtu Americas"), pursuant to which Virtu Americas will act as Nuveen Securities' sub-placement agent with respect to at-the-market offerings of Common Shares pursuant to the Prospectus Supplement. Accordingly, effective immediately, each reference to the applicable sales agent as Nuveen Securities' sub-placement agent in the Fund's Prospectus Supplement is hereby replaced with "Virtu Americas" and the Prospectus Supplement is further amended as follows:

The Fund will compensate Nuveen Securities with respect to sales of Common Shares at a variable commission rate. The variable commission rate shall be equal to the sum of (i) seventy-five percent (75%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.80% of the aggregate gross sales proceeds and (ii) twenty-five percent (25%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.20% of the aggregate gross sales proceeds. Out of this commission, Nuveen Securities will compensate the applicable dealer at a variable commission rate equal to seventy-five percent (75%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.80% of the aggregate gross sales proceeds. In connection with the sale of the Common Shares on the Fund's behalf, Nuveen Securities may be deemed to be an "underwriter" within the meaning of the Securities Act and the compensation of Nuveen Securities may be deemed to be underwriting commissions or discounts.

The Fund will compensate Nuveen Securities with respect to sales of Common Shares at a variable commission rate. The variable commission rate shall be equal to the sum of (i) seventy-five percent (75%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.80% of the aggregate gross sales proceeds and (ii) twenty-five percent (25%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.20% of the aggregate gross sales proceeds. "Gross sales proceeds" with respect to each sale of Common Shares shall be the gross sales price per Common Share multiplied by the number of Common Shares sold. The gross sales price with respect to each sale of Common Shares sold pursuant to the Distribution Agreement shall be the gross sales price per Common Share of such Common Shares. Nuveen Securities will compensate Virtu Americas as sub-placement agent at a variable commission rate equal to seventy-five percent (75%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.80% of the aggregate gross sales proceeds. Settlements of sales of Common Shares will occur on the first business day following the date on which any such sales are made.

The Fund will compensate Nuveen Securities with respect to sales of Common Shares at a variable commission rate. The variable commission rate shall be equal to the sum of (i) seventy-five percent (75%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.80% of the aggregate gross sales proceeds and (ii) twenty-five percent (25%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.20% of the aggregate gross sales proceeds. "Gross sales proceeds" with respect to each sale of Common Shares shall be the gross sales price per Common Share multiplied by the number of Common Shares sold. The gross sales price with respect to each sale of Common Shares sold pursuant to the Distribution Agreement shall be the gross sales price per Common Share of such Common Shares. Nuveen Securities will compensate Virtu Americas as sub-placement agent at a variable commission rate equal to seventy-five percent (75%) of the premium to net asset value with respect to the sale of any Common Shares sold until such compensation is equal to 0.80% of the aggregate gross sales proceeds. Settlements of sales of Common Shares will occur on the first business day following the date on which any such sales are made.

PLEASE KEEP THIS WITH YOUR

FUND'S PROSPECTUS SUPPLEMENT FOR FUTURE REFERENCE

EGN-NMZP-0426P