Filed Pursuant to Rule 424(b)(3)

File No. 333-253965

NUVEEN MUNICIPAL HIGH INCOME OPPORTUNITY FUND

(NYSE: NMZ)

(THE “FUND”)

SUPPLEMENT DATED JUNE 1, 2021

TO THE FUND’S STATEMENT OF ADDITIONAL

INFORMATION (“SAI”) DATED MARCH 5, 2021

Effective June 1, 2021, Amy B. R. Lancellotta and Joanne T. Medero are appointed to the Fund’s Board of Trustees (the “Board”) as independent trustees. In addition, Ms. Lancellotta is appointed as a member of the Board’s Closed-End Funds Committee, Nominating and Governance Committee, and Compliance, Risk Management and Regulatory Oversight Committee, and Ms. Medero is appointed as a member of the Nominating and Governance Committee and Compliance, Risk Management and Regulatory Oversight Committee.

The changes described below are made to the Fund’s SAI effective immediately.

1. The following information is added to the table under the section entitled “Trustees and Officers” under “Management of the Fund”:

Name, Business Address and Year of Birth	Position(s) Held with Fund	Term of Office and Length of Time Served with Funds in the Fund Complex	Principal Occupation(s) During Past Five Years	Number of Portfolios in Fund Complex Overseen By Trustee	Other Directorships Held by Trustee During Past Five Years
Amy B. R. Lancellotta 333 West Wacker Drive Chicago, IL 60606 (1959)	Trustee	Term—Class II Length of Service— Since 2021	Formerly, Managing Director, Independent Directors Council (IDC) (supports the fund independent director community and is part of the Investment Company Institute (ICI), which represents regulated investment companies) (2006-2019); formerly, various positions with ICI (1989-2006); Member of the Board of Directors, Jewish Coalition Against Domestic Abuse (JCADA) (since 2020).	143	None

1

Joanne T. Medero 333 West Wacker Drive Chicago, IL 60606 (1954) Trustee Term—Class III Length of Service— Since 2021 Formerly, Managing Director, Government Relations and Public Policy (2009-2020) and Senior Advisor to the Vice Chairman (2018-2020), BlackRock, Inc. (global investment management firm); formerly, Managing Director, Global Head of Government Relations and Public Policy, Barclays Group (IBIM) (investment banking, investment management and wealth management businesses) (2006-2009); formerly, Managing Director, Global General Counsel and Corporate Secretary, Barclays Global Investors (global investment management firm) (1996-2006); formerly, Partner, Orrick, Herrington & Sutcliffe LLP (law firm) (1993-1995); formerly, General Counsel, Commodity Futures Trading Commission (government agency overseeing U.S. derivatives markets) (1989-1993); formerly, Deputy Associate Director/Associate Director for Legal and Financial Affairs, Office of Presidential Personnel, The White House (1986-1989); Member of the Board of Directors, Baltic-American Freedom Foundation (seeks to provide opportunities for citizens of the Baltic states to gain education and professional development through exchanges in the U.S.) (since 2019). 143 None

2. The following information is added under “Board Diversification and Trustee Qualifications”:

Amy B. R. Lancellotta. After 30 years of service, Ms. Lancellotta retired at the end of 2019 from the Investment Company Institute (ICI), which represents regulated investment companies on regulatory, legislative and securities industry initiatives that affect funds and their shareholders. From November 2006 until her retirement, Ms. Lancellotta served as Managing Director of ICI’s

2

Independent Directors Council (IDC), which supports fund independent directors in fulfilling their responsibilities to promote and protect the interests of fund shareholders. At IDC, Ms. Lancellotta was responsible for all ICI and IDC activities relating to the fund independent director community. In conjunction with her responsibilities, Ms. Lancellotta advised and represented IDC, ICI, independent directors and the investment company industry on issues relating to fund governance and the role of fund directors. She also directed and coordinated IDC’s education, communication, governance and policy initiatives. Prior to serving as Managing Director of IDC, Ms. Lancellotta held various other positions with ICI beginning in 1989. Before joining ICI, Ms. Lancellotta was an associate at two Washington, D.C. law firms. In addition, since 2020, she has been a member of the Board of Directors of the Jewish Coalition Against Domestic Abuse (JCADA), an organization that seeks to end power-based violence, empower survivors and ensure safe communities. Ms. Lancellotta received a B.A. degree from Pennsylvania State University in 1981 and a J.D. degree from the National Law Center, George Washington University (currently known as George Washington University Law School) in 1984.

Joanne T. Medero. Ms. Medero has over 30 years of financial services experience and, most recently, from December 2009 until her retirement in July 2020, she was a Managing Director in the Government Relations and Public Policy Group at BlackRock, Inc. (BlackRock). From July 2018 to July 2020, she was also Senior Advisor to BlackRock’s Vice Chairman, focusing on public policy and corporate governance issues. In 1996, Ms. Medero joined Barclays Global Investors (BGI), which merged with BlackRock in 2009. At BGI, she was a Managing Director and served as Global General Counsel and Corporate Secretary until 2006. Then, from 2006 to 2009, Ms. Medero was a Managing Director and Global Head of Government Relations and Public Policy at Barclays Group (IBIM), where she provided policy guidance and directed legislative and regulatory advocacy programs for the investment banking, investment management and wealth management businesses. Before joining BGI, Ms. Medero was a Partner at Orrick, Herrington & Sutcliffe LLP from 1993 to 1995, where she specialized in derivatives and financial markets regulation issues. Additionally, she served as General Counsel of the Commodity Futures Trading Commission (CFTC) from 1989 to 1993 and, from 1986 to 1989, she was Deputy Associate Director/Associate Director for Legal and Financial Affairs at The White House Office of Presidential Personnel. Further, from 2006 to 2010, Ms. Medero was a member of the CFTC Global Markets Advisory Committee and she has been actively involved in financial industry associations, serving as Chair of the Steering Committee of the SIFMA (Securities Industry and Financial Markets Association) Asset Management Group (2016-2018) and Chair of the CTA (Commodity Trading Advisor), CPO (Commodity Pool Operator) and Futures Committee of the Managed Funds Association (2010-2012). Currently, Ms. Medero chairs the Corporations, Antitrust and Securities Practice Group of The Federalist Society for Law and Public Policy (since 2010 and from 2000 to 2002). In addition, since 2019, she has been a member of the Board of Directors of the Baltic-American Freedom Foundation, which seeks to provide opportunities for citizens of the Baltic states to gain education and professional development through exchanges in the United States. Ms. Medero received a B.A. degree from St. Lawrence University in 1975 and a J.D. degree from the National Law Center, George Washington University (currently known as George Washington University Law School) in 1978.

3

3. The following information is added to the table under the section entitled “Share Ownership”:

Name of Trustee	Dollar Range of Equity Securities in the Fund	Aggregate Dollar Range of Equity Securities in All Registered Investment Companies Overseen by Trustee in Family of Investment Companies
Amy B. R. Lancellotta1	None	None
Joanne T. Medero1	None	None

¹ Information is provided as of the date of this Supplement.

PLEASE KEEP THIS WITH YOUR

FUND’S STATEMENT OF ADDITIONAL INFORMATION

FOR FUTURE REFERENCE

4