Exhibit 12.(a)(1)(iv)

Offer by

MORGAN STANLEY CHINA A SHARE FUND, INC.

To Purchase for Cash
up to 20% of the Fund’s Outstanding Shares of
Common Stock

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 11:59 P.M.,
NEW YORK TIME, ON FEBRUARY 20, 2024 (“TERMINATION DATE”)

THIS OFFER IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES BEING TENDERED, BUT IS SUBJECT TO OTHER CONDITIONS AS OUTLINED IN THE ISSUER TENDER OFFER STATEMENT AND IN THE LETTER OF TRANSMITTAL.

January 22, 2024

To Our Clients:

Enclosed for your consideration is the Issuer Tender Offer Statement, dated January 22, 2024, of Morgan Stanley China A Share Fund, Inc., a Maryland corporation registered under the Investment Company Act of 1940, as amended, as a closed-end, non-diversified management investment company (the “Fund”), and a related Letter of Transmittal (which together constitute the “Offer”), pursuant to which the Fund is offering to purchase up to 20% of the Fund’s outstanding shares of common stock, par value $0.01 per share (the “Shares”), upon the terms and conditions set forth in the Offer.

The Issuer Tender Offer Statement and the Letter of Transmittal are being forwarded to you for your information only and cannot be used by you to tender Shares held by us for your account. We are the holder of record of Shares held for your account. A tender of such Shares can be made only by us as the holder of record and only pursuant to your instructions.

Your attention is called to the following:

(1) The purchase price to be paid for the Shares is an amount per Share, net to the seller in cash, equal to 98.5% of the net asset value per Share as determined by the Fund at the close of regular trading on the New York Stock Exchange on February 21, 2024, or the business day following such later date to which the Offer is extended. The current net asset value of the Fund is calculated daily and may be obtained by calling Georgeson LLC, the Fund’s Information Agent, toll free at 888-355-3492 or by calling the Fund toll free at 800-231-2608.

(2) The Offer is not conditioned upon any minimum number of Shares being tendered.

(3) Upon the terms and subject to the conditions of the Offer, the Fund will purchase all Shares validly tendered on or prior to 11:59 p.m., New York time, on February 20, 2024, or such later date to which the Offer is extended (the “Termination Date”).

(4) No fees or commission will be payable to the Fund in connection with the tender offer. However, tendering Stockholders may be obligated to pay brokerage commissions or, subject to Instruction 6, “Stock Transfer Taxes,” of the Letter of Transmittal, stock transfer taxes on the purchase of Shares by the Fund pursuant to the Offer.

(5) Your instructions to us should be forwarded in ample time before the Termination Date to permit us to submit a tender on your behalf.

1

An envelope to return your instructions to us is enclosed. YOUR INSTRUCTIONS TO US SHOULD BE FORWARDED AS PROMPTLY AS POSSIBLE IN ORDER TO PERMIT US TO SUBMIT A TENDER ON YOUR BEHALF IN ACCORDANCE WITH THE TERMS AND CONDITIONS OF THE OFFER.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making or acceptance of the Offer would not be in compliance with applicable law.

Neither the Fund nor its Board of Directors is making any recommendation to any Stockholder whether to tender or refrain from tendering Shares in the Offer. Each Stockholder is urged to read and evaluate the Offer and accompanying materials carefully.

2

INSTRUCTIONS

The undersigned acknowledge(s) receipt of your letter, and the enclosed Offer, dated January 22, 2024, relating to the offer by the Fund to purchase up to 20% of the Fund’s outstanding Shares.

This will instruct you to tender to the Fund the number of Shares indicated below (which are held by you for the account of the undersigned), upon the terms and subject to the conditions set forth in the Offer that you have furnished to the undersigned.

AGGREGATE NUMBER OF SHARES TO BE TENDERED:

__________ Shares

ENTER NUMBER OF SHARES TO BE TENDERED.

3