NUVEEN MUNICIPAL HIGH INCOME OPPORTUNITY FUND

(NYSE: NMZ)

(THE “FUND”)

SUPPLEMENT DATED MARCH 24, 2020

TO THE FUND’S PROSPECTUS DATED FEBRUARY 28, 2020

The following replaces any references contained in the Prospectus with respect to the Fund’s net asset value (“NAV”) per Common Share, market price, percent of premium/(discount) to NAV per Common Share, number of shares outstanding, and net assets:

The NAV per Common Share, the market price and percent of premium/(discount) to NAV per Common Share on March 23, 2020, were $11.31, $10.35 and (8.49)%, respectively. As of March 23, 2020, the Fund had 78,965,215 Common Shares outstanding, 870 AMTP Shares and net assets applicable to Common Shares of $893,114,731.

In addition, the following disclosure is added to the sections entitled “Prospectus Summary – Special Risk Considerations – Other Risks – Recent Market Conditions” and “Risk Factors – Other Risks – Recent Market Conditions”:

National and regional economies and financial markets are becoming increasingly interconnected, which increases the possibilities that conditions in one country, region or market might adversely impact issuers in a different country, region or market. Changes in legal, political, regulatory, tax and economic conditions may cause fluctuations in markets and securities prices around the world, which could negatively impact the value of the Fund’s investments. Major economic or political disruptions, particularly in large economies like China’s, may have global negative economic and market repercussions. Additionally, events such as war, terrorism, natural and environmental disasters and the spread of infectious illnesses or other public health emergencies may adversely affect the global economy and the markets and issuers in which the Fund invests. Recent examples of such events include the outbreak of a novel coronavirus known as COVID-19 that was first detected in China in December 2019 and heightened concerns regarding North Korea’s nuclear weapons and long-range ballistic missile programs. These events could reduce consumer demand or economic output, result in market closure, travel restrictions or quarantines, and generally have a significant impact on the economy. These events could also impair the information technology and other operational systems upon which the Fund’s service providers, including the investment adviser and sub-adviser, rely, and could otherwise disrupt the ability of employees of the Fund’s service providers to perform essential tasks on behalf of the Fund. Governmental and quasi-governmental authorities and regulators throughout the world have in the past responded to major economic disruptions with a variety of significant fiscal and monetary policy changes, including but not limited to, direct capital infusions into companies, new monetary programs and dramatically lower interest rates. An unexpected or quick reversal of these policies, or the ineffectiveness of these policies, could increase volatility in securities markets, which could adversely affect the fund’s investments.

PLEASE KEEP THIS WITH YOUR FUND’S PROSPECTUS

FOR FUTURE REFERENCE