The prospect of rising interest rates shutting off the economic recovery sent an edgy stock market tumbling today. The Dow Jones Industrial Average fell 20.23 points.

Following close on the heels of Friday's announcement of a $1.2 billion increase in M1, the money supply figure, came word early today that several major banks had raised their prime lending rates from 10 1/2 percent to 11 percent. Both events served to heighten Wall Street concerns about rising interest rates.

As a result of those two events, the Dow industrials--the most closely watched market barometer--dropped by more than 12 points in the first hour of trading. The market continued its fall during the day, with the average closing at 1,163.06, its lowest closing since mid-April.

"The worry now is that the recovery is in jeopardy," said James Balog, director of research at Drexel Burnham Lambert Inc. "It's a very jittery market and there's plenty of skepticism because we're living in the shadow of a very, very difficult period. There are still plenty of problems out there."

Losses were broad in trading as 1,312 stocks on the New York Stock Exchange fell today and only 338 gained. Only three of the 30 stocks that make up the Dow industrials gained today as another 24 declined. Three issues were unchanged.

Over the last two weeks, stocks prices have steadily given ground with the Dow industrials having lost more 80 points. "This market is beginning to break down on a broad basis," said Monte Gordon, vice president at The Dreyfus Corp.

But market experts pointed out that, with volume today at only 71.4 million shares--a relatively light trading day by recent measures, compared with 67.8 million Friday--there is little evidence of a major market slide. "It hasn't become a selling stampede yet, but it could," Gordon said. "The volume tends to indicate that there is no sign of bargain hunting yet."

The Standard & Poors 500 index fell by 2.56 point to 159.18, while the S&P 400 dropped 2.93 points to 179.47. The New York exchange composite index was down 1.41 points, closing at 92.19, and the average price per share fell by 53 cents.

Of the widely traded issues, General Motors was off 3 1/8, closing at 66. Technology stocks were particular losers today, with Texas Instruments off 2 1/2, closing at 102 1/2, Tandy off 2 3/8 at 40 3/8 and Digital Equipment off 2 1/4, closing at 103 1/4. Metromedia fell 65 points to close at 435 after an article highly critical of the company's accounting practices was published over the weekend in Barron's magazine.

On other stock exchanges, the American Stock Exchange's index fell 3.88 points to 227.54 as volume rose to 6.2 million shares from Friday's 5.9 million. The average price per share fell 28 cents as 126 stocks gained and 531 declined. Another 166 issues were unchanged.

In over the counter trading, the Nasdaq composite index dropped 5.27 points to 294.93 as 1,349 Nasdaq issues declined and only 294 advanced. Another 2,019 stocks were unchanged.