Supreme Court Justice Harry A. Blackmun, who has been the target of frequent death threats since he wrote the court's controversial 1973 decision legalizing abortion, said yesterday that a bullet was fired through a window of his Arlington apartment Thursday night.

Virginia and federal law enforcement officials said they are investigating the possiblility that an antiabortion group may have been responsible for the shooting.

Both Blackmun and his wife, Dorothy, were at home at the time, but neither was injured by the single shot, which a law enforcement source said showered glass on Dorothy Blackmun as she sat in the living room of the Blackmuns' third-floor apartment. The source said Blackmun had just left the room when the shot was fired.

Lane Bonner, an FBI spokesman, said yesterday that a 9-mm bullet, which could have been fired by a pistol or a rifle, was recovered from a chair in the apartment. Other law enforcement sources said the shot left a hole in the window about the size of a baseball.

Although police said they had no suspects last night, Bonner said, "We are looking seriously at threatening letters from antiabortion groups, especially a recent one."

Bonner declined to comment further on the letter, but law enforcement officials said that Blackmun received a particularly graphic death threat in the past week.

Blackmun, who was hearing cases at the court yesterday, has been the target of numerous threats from antiabortion groups ever since he wrote the landmark Roe v. Wade decision that overturned antiabortion laws. Supreme Court officials said the justice routinely turns the threatening letters over to the police.

In the past, Blackmun has said he received mail calling him "Butcher of Dachau, murderer, Pontius Pilate, King Herod, you name it."

Both Arlington police and the FBI were informed immediately after last week's shooting. It became public yesterday after Blackmun released a brief statement in response to a query from a United Press International reporter.

"A shot went through the window of the Blackmun home last Thursday, Feb. 28," the statement said. "No one was injured. The matter is under investigation."

The FBI conducted a forensic analysis of the evidence this weekend, but results have not been made public.

Blackmun, 76, appointed to the court in 1970 by President Nixon, has been placed under constant police protection, according to Wanda Martinson, the justice's secretary, and all his mail is screened.

Security was first stepped up for Blackmun in October after he received a threatening letter, purportedly from a small antiabortion group called the "Army of God." The group, three of whose members were convicted last year of the kidnaping of an Illinois abortion clinic director, has claimed attacks on abortion clinics around the country.

The shooting in Arlington comes six weeks after the 12th anniversary of the Roe v. Wade case, and at the end of a year-long period in which seven abortion clinics and related facilities in the Washington area have been hit by bomb blasts.

In January, more than 70,000 opponents of abortion gathered on the steps of the Supreme Court to protest the decision. President Reagan spoke to the crowd by loudspeaker hookup and encouraged them to "end the national tragedy of abortion."

The president also condemned the recent violence at the clinics, as have several other major figures in the antiabortion movement, including Moral Majority leader the Rev. Jerry Falwell.

Blackmun has said that being a justice is a "rotten way to earn a living" and has noted that abortion foes have picketed him regularly since the 1973 decision.