Company: MYI
Filing Date: 2025-07-15
Form Type: 425
Source: 0001193125-25-159406
Chunk: 1

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-07-15
Form: 425
Chunk 1
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 the Offer be extended beyond August 15, 2025, the
Pricing Date will be the close of ordinary trading on the NYSE on the next day the NAV is calculated after the newly designated Expiration Date. Stockholders who choose to participate in the Offer can expect payments for Shares tendered and accepted
to be made within approximately five business days after the Expiration Date.

The Shares are traded on the NYSE under the symbol
“MVF.” As of July 8, 2025, the Fund had 57,335,699 Shares outstanding; its NAV per Share was $7.21 and its market price per Share was $6.58, representing a discount to NAV of (8.74)%. The NAV on the Pricing Date may be higher or lower
than the NAV as of July 8, 2025, and the discount to NAV at which the Shares trade may be greater or lesser than the discount as of July 8, 2025. For the Fund’s most current NAV and market price per Share, you may view online at https://www.blackrock.com/us/individual/products/240201/blackrock-munivest-fund-inc-usd-fund. For additional questions or information during the pendency of this Offer, you may contact Georgeson LLC (the“Information Agent”) by calling (866) 961-8329,between the hours of 9:00a.m. and 11:00p.m., Eastern time, Monday through Friday (except holidays), and 12:00p.m. and 6:00p.m., Eastern time, on Saturday.

The Offer is subject to important terms and conditions, including the conditions listed under Section 4, “Certain Conditions of the Offer.”

Neither the Securities and Exchange Commission (the “Commission”) nor any state securities commission has approved or disapproved of the Offer, passed upon the fairness or merits of the Offer, or determined whether this Offer to Purchase is accurate or complete. Any representation to the contrary is a crime.

If you are not interested in selling any of your Shares at this time, you do not need to do anything. This Offer is not part of a plan to liquidate the Fund. Stockholders are not required to participate in the Offer.

You should be aware that, if you tender Shares pursuant to the Offer, Shares tendered and accepted into the Offer will not be entitled to receive any Fund dividend or distribution with a record date on or after August 22, 2025