Stock prices plummeted today as the euphoria that gripped investors following Ronald Reagan's election began to be replaced by wariness over rapidly climbing interest rates and inflation.

The Dow Jones industrial average fell 23.89 points to 969.45. It was the biggest one-day decline in that closely watched stock market guage since Oct. 9, 1979.

Today's big decline came after several weeks of strong gains in the stock market following Reagan's election -- as investors gleefully shrugged off bad economic news, sending the Dow average over the vaunted 1,000-barrier at one point.

"You can only overlook interest rates for so long," said Burton H. Siegel, director of research for the brokerage firm Drexel Burnham Lambert Inc. Many analysts fear that the recent sharp climb in interest rates will choke off the nascent economic recovery.

If that happens, corporate profits will decline, which hurts the price of stocks.

Interest rates have been rising sharply in part because the Federal Reserve Board has been conducting a tight monetary policy in an attempt to hold down the growth of the money supply to fight inflation. Shortly after the New York Stock Exchange shut down, however, the Federal Reserve announced that the money supply fell sharply last week, a report that should buoy investors.

Stock prices started declining from the opening bell and continued to fall all day, except for a brief, futile rally try late in the morning. The Dow average closed at its slowest level of the day.

"But there was no panic selling," said Siegel of Drexel Burnham. Although trading volume was high by historical standards -- 48.6 million shares were exchanged on the NYSE -- it is not high when compared with the levels reached in recent weeks. Four of the five busiest days in New York Stock Exchange history have occurred since the presidential election.

The decline was exacerbated by what market analysts call "profit-taking." Despite today's sharp decline, the Dow average remains about 35 points higher than a month ago and many investors are selling stocks to realize the paper profits they have accrued in the past 30days.

So-called technical analysts of the market, who think the behavior of stock prices has more to do with regular internal developments in the market rather than outside influences like the economy, have been warning that a sharp decline was overdue.

As Newton Zinder of E.F. Hutton & Co. pointed out, last Friday, when the Dow average gained 3.66, all the gain was accounted for by just two stocks: International Paper and Texaco. When strength in a few stocks masks weakness in many, technical analysts predict an overall decline.

Whether today's decline is the early stage of a sustained fall or merely one day of setback in the middle of a continued rally is debated sharply by Wall Street analysts.

"We've had these one-day things in the past, and the market has stabilized and started back up," said Siegel. While the market rallied sharply in the weeks following Reagan's election, the current rally began last April. In the past 6 1/2 months, the Dow Jones average has climbed more than 200 points.

Oil stocks, which had led much of the recent rally in the market, fell today, as did most other stocks on the New York exchange, where declines numbered 1,316 and gainers totaled 351.

Standard Oil of Indiana fell 5 1/4 to 91 5/8; Standard Oil of California slipped 6 3/4 to 107 3/4: Mobil dropped 3 1/8 to 64 3/4, while Gulf declined 2 7/8 to 49 3/4.

Other major stocks registering big declines included General Motors, off 1 3/4 to 42 3/4; General Electric, down 1 3/4 to 60 1/8; and American Telephone & Telegraph, down 5/8 to 46 7/8.

On the American Stock Exchange, the index fell 5.72 points to 365.03, with 499 stocks closing lower and 162 stocks higher.

In the over-the-counter market, the National Association of Securities Dealers' index was off 3.24 points to 204.91.