An American businessman was dragged out of his car by Soviet police here Monday night and arrested on charges of smuggling, U.S. Embassy officials said yesterday.

F. Jay Crawford, 38, Moscow representative of International Harvester Co. was arrested as he and his fiance, an employe of the U.S. Embassy, were driving through downtown Moscow to a cocktail party at a friend's apartment.

U.S. sources said Soviet policemen suddenly appeared when Crawford stopped his car at a traffic light. The policemen reportedly yanked open the door of the car and dragged Crawford out. The sources said his screaming fiance, Virginia Olbrish, 32, grabbed the car keys and invoked diplomatic immunity when the policemen also tried to drag her from the car.

Although the incident took place around 7 p.m. Monday, the Soviet Foreign Ministry refused to respond to U.S. Embassy queries about Crawford's whereabouts and condition until late yesterday.

The ministry permitted U.S. consul Clifford Gross to visit Crawford at Moscow's Lefortovo Prison late yesterday. Soviet officials said the American is held not only on smuggling charges but also possible currency violations. Under the Soviet criminal code these charges carry prison terms of three to 10 years.

The U.S. Embassy protested the Foreign Ministry's conduct. It was reliably reported that Crawford, who has been here since August 1976, denied all the allegations against him.

International Harvester is one of the top companies in annual trade figures doing business with the Soviets. Its chairman, Brooks McCormick, is a director of the U.S.-U.S.S.R. Trade and Economic Council, which seeks to promote more trade between the two countries. McCormik has been an ardent supporter of increased commerce between the two superpowers.

[McCormick yesterday requested that "the U.S. government take immediate steps to secure (Crawford's) release." The message was relayed by Rep. Dan Rostenkowski (D-Ill.) to Vice President Mondale.]

The arrest is the latest in series of incidents of increasing seriousness involving official Soviet government actions against Americans.

Several informed Western diplomatic sources speculated last night that Crawford's arrest is the beginning of a Soviet effort to arrange a swap for two Soviet U.N. employes now held in the Unites States on conspiracy charges for allegedly plotting to transmit U.S. Navy secrets to Moscow.

Several sources also suggested that the Soviets may have deliberately chosen a man without diplomatic immunity since the two arrested Soviet U.N. officials do not enjoy diplomatic status.

The incident comes against a back-drop of deteriorating relations between Washington and Moscow as the Carter administration reviews its approach to dealing with the Soviet leadership.

Just Monday, the Soviet government newspaper Izvestia accused a former woman employe of the U.S. Embassy, Martha D. Peterson, of being an accomplice in a CIA plot to "stop detente" that allegedly involved the slaying of a Soviet citizen and obtaining presumably secret information to be passed to the West.

In recent weeks the two countries have exchanged increasingly sharp criticisms of each other's policies and the strategic arms limitations negotiations, cornerstone of Soviet-American relations, apparently have stalled anew in complex disagreements.

According to the account from U.S. sources, the latest incident took place near the Kievsky railroad station when Crawford and Olbrish pulled up in their Volvo station wagon to a stoplight. They reportedly waited for a lengthy time for the light to turn green, when suddenly Soviet police appeared and seized Crawford, a rangy, moustachoied Alabaman. Olbrish, a secretary-archivist at the embassy, was left behind after the police scuffled with Crawford and took him away.

She flagged passing car and was taken to the U.S. Embassy several blocks away where she reported the incident. She was reported to be still upset yesterday.

Western diplomatic sources here viewed the incident as "without doubt the most serious of its kind in many years." Some recalled the 1963 Soviet seizure of a Soviet studies professor Frederick Barghoorn, for a similar precedent. Barghoorn was released after strenuous protests by President Kennedy.

"When their hand is caught in the cookie jar, the Russians can react this way," said one source, speaking of the possibility that the Crawford case is a preliminary to a swap. "But remember, there are two Soviets in jail and so far, only one American." It was a comment made several times by other sources last night.

The smuggling allegation involves Article 78 of the criminal code dealing with smuggling and contraband brought in over Soviet borders. The possible currency allegation involves Article 88 of the same code.

International Harvester has had substantial business with the Soviets in the past, selling them an estimated 1,200 major earthmoving and construction machines including spare parts. The company's sales here since 1974 exceed $300 million.

Crawford, said by friends here to be an expert troubleshooter on mechanical problems of such machines, was brought in two year ago to help run the spare parts contracts.

Soviets traditionally are wary of allowing foreigners to move widely within the country and Crawford was reportedly allowed only infrequent contract with Soviet mechanics who were actually servicing the machines.

In the past several years, International Harvester and many other U.S. firms that opened offices here in the early 1970s in anticipation of major sales to the Soviets have been disappointed. Soviet harvest shortfalls have forced the Soviets to use hard currency to buy feed grains, with a resultant cutback in Western equipment purchases. International Harvester had recently recalled its resident director here and Crawford was serving as temporary head of the office when he was seized.