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:
| 1. | The third paragraph on the cover page of the Prospectus Supplement is hereby deleted and replaced with
the following: |
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.
| 2. | The second paragraph in the section of the Prospectus Supplement titled “Prospectus Supplement Summary
– The Offering” is hereby deleted and replaced with the following: |
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.
| 3. | The fourth paragraph in the section of the Prospectus Supplement titled “Plan of Distribution”
is hereby deleted and replaced with the following: |
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
