Wall Street's latest stock market rally came to a screeching halt today when hints of rising interest rates sent prices sliding.

The Dow Jones industrial average dropped 5.81 points to close at 1,140.09. The Dow had hit a new all-time high of 1,145.90 Thursday.

The NYSE index dropped 0.39 point to 87.81, and the price of an average share was off 15 cents.

Floor volume was about 77.33 million shares, down from 92.34 million Thursday. Turnover of NYSE stocks nationwide was 89.06 million compared with 107.69 million Thursday.

The American Stock Exchange index was up 1.03 points at 386.03, and the price of an average share gained 4 cents. Composite volume was 8.50 million shares compared with 9.46 million Thursday.

The National Association of Securities Dealers Nasdaq index of over-the-counter stocks rose 0.52 point to a record 270.89.

Some analysts said investors were staying on the sidelines, waiting for the latest figures on the money supply before making any new commitments. The market has always reacted strongly to any indication the Federal Reserve may restrict the swollen money supply, thus forcing up interest rates.

Henry Kaufman, the influential Salomon Brothers economist, helped fuel this worry when he suggested that the Fed is moving cautiously to tighten the money supply and may have to be more aggressive if it wants to succeed.

Given the market's recent climb, which included a 17.90-point jump in the Dow on Wednesday, a drop in prices was not unexpected, said Monte Gordon of Dreyfus Corp. "The market had a pretty good run. I'd be inclined to regard this in the context of a normal retracement," he said.

Among hospital-management stocks, Humana climbed 1 7/8 to 36 7/8, Hospital Corp. of America was up 3 1/8 to 51 1/4, AMI Inc. rose 2 1/4 to 32 1/8, and National Medical Enterprises went up 1 7/8 to 36 1/2.

David J. Lothson, an analyst who follows the industry for Kidder, Peabody & Co., said investors viewed provisions for Medicare reimbursement in the Social Security bill passed by Congress as a prospective boon to private-hospital profits.

Dart & Kraft climbed 2 7/8 to 74 1/4, hitting a new high since the company's formation in 1980 through a merger of Dart Industries and Kraft. The company described its first-quarter earnings prospects as "solid" with the help of some "very encouraging" trends in its appliance and laminates businesses.