Company: MYI
Filing Date: 2025-10-03
Form Type: N-CSR
Source: 0001193125-25-230138
Chunk: 0

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-10-03
Form: N-CSR
Chunk 0
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UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM N-CSR

CERTIFIED SHAREHOLDER REPORT OF REGISTERED MANAGEMENT

INVESTMENT COMPANIES

Investment Company
Act file number: 811-06540

Name of Fund: BlackRock MuniYield Quality Fund III, Inc. (MYI)

Fund Address: 100 Bellevue Parkway, Wilmington, DE 19809

Name and address of agent for service: John M. Perlowski, Chief Executive Officer, BlackRock MuniYield Quality Fund III, Inc., 50 Hudson Yards, New York,
NY 10001

Registrant’s telephone number, including area code: (800) 882-0052, Option 4

Date of fiscal year end: 07/31/2025

Date of reporting period:
07/31/2025

| Item 1 – | Reports to Stockholders |

(a) The Reports to Shareholders are attached herewith.

July 31, 2025

| 2025 Annual Report |

| BlackRock Long-Term Municipal Advantage Trust (BTA) |
| BlackRock MuniAssets Fund, Inc. (MUA)               |
| BlackRock MuniYield Fund, Inc. (MYD)                |
| BlackRock MuniYield Quality Fund, Inc. (MQY)        |
| BlackRock MuniYield Quality Fund III, Inc. (MYI)    |

| Not FDIC Insured • May Lose Value • No Bank Guarantee |

Table of Contents

Page

| AnnualReport:                                           |     |
| Municipal Market Overview                               |   3 |
| The Benefits and Risks of Leveraging                    |   4 |
| Derivative Financial Instruments                        |   4 |
| Fund Summary                                            |   5 |
| Financial Statements:                                   |     |
| Schedules of Investments                                |  20 |
| Statements of Assets and Liabilities                    |  62 |
| Statements of Operations                                |  64 |
| Statements of Changes in Net Assets                     |  66 |
| Statements of Cash Flows                                |  69 |
| Financial Highlights                                    |  71 |
| Notes to Financial Statements                           |  80 |
| Report of Independent Registered Public Accounting Firm |  93 |
| Important Tax Information                               |  94 |
| Disclosure of Investment Advisory Agreements            |  95 |
| Investment Object