A powerful explosion last night partly destroyed an American-owned factory here that produces the guidance system for cruise missiles and that has been the target of Canadian antinuclear protesters in recent years.

The explosion at the Litton Systems of Canada Ltd. plant injured four factory workers and three policemen who were following up an anonymous phone tip when the explosion occurred. It left the front of the suburban building in ruins, and operations there were suspended.

Police said late today that no one had claimed responsibility. "We have no leads at all in the case," said a spokesman. Another estimated the damages as "in the millions."

The plant, a subsidiary of Litton Industries of Beverly Hills, Calif., has been the scene of numerous demonstrations, and the company is said to have received three or four bomb threats previously.

"We have no idea who did it," The Associated Press quoted Litton Industries spokesman Robert Knapp as saying at the company's California headquarters. He said he knew of no previous threats to the plant.

An estimated 300 to 500 pounds of dynamite was cached in an orange-colored box, marked "Danger Explosives," beside a blue van that had been parked in front of the plant. The bomb exploded at 11:31 p.m., 13 minutes after a woman phoned police that an explosive device was about to go off. It detonated after police had approached the vehicle. Three of the injured remained in hospital.

Only hours before last night's blast, a group of Canadian nuclear protesters charged with trespassing on Litton property in a recent demonstration lost a legal battle to force the firm's executives to testify at their trial before a court in Ontario Province.

A group of 22 defendants had tried to call the officials to the stand allegedly to support their claim that Litton's business is a crime against mankind that justified the protesters' attempts to shut down the Toronto factory. The Ontario Court of Appeal upheld a lower court decision to quash subpoenas for five Litton executives.

Today, leaders of various antinuclear groups in Canada disavowed any connection with the blast. James Stark, president of Operation Dismantle, one of the larger antinuclear lobbies, said no protest group in Canada could be behind the bombing because all such organizations are nonviolent.

Stark suggested that Litton may be the victim of some new and violent element in the peace movement, perhaps with international connections. Demonstrations in Western Europe against nuclear weapons, including those to be carried by the cruise missile, have included violent factions.

Stark was instrumental in having a call for disarmament put on the ballot for the next local election in the Canadian capital, Ottawa. Similar moves have followed in 40 other localities.

In 1979, Litton won a $1 billion contract to produce 5,500 guidance systems for the cruise, which is being developed for deployment by the United States--under NATO--in Western Europe.

The missile has inspired considerable agitation in Canada since it was revealed earlier this year that the government of Prime Minister Pierre Elliott Trudeau was consulting with the Reagan administration about plans to test the weapons system in western Canada. Terrain there is similar to that which would be encountered if the missile were launched over the Soviet Union, U.S. officials say. The craft is powered by an air-breathing engine.