The suspect was named as Stig Engstrom, a former advertising consultant known for his staunch opposition to Palme's leftwing policies and who is now dead.
Palme was gunned down on the evening of February 28, 1986 after leaving a Stockholm cinema with his wife, having dismissed his bodyguards for the evening.
He was shot in the back by his assailant, who fled the scene and left the 59-year-old dying in a pool of blood on the sidewalk.
The gruesome murder shocked Swedes, and the country is said to have "lost its innocence" that day.
More than 10,000 people have been questioned over the years, and 134 people have confessed to the crime though none have been successfully tied to the murder.
Chief prosecutor Krister Petersson said they had zeroed in on Engstrom as the main suspect.
"Because he is dead, I can't press charges against him, and have therefore decided to close the investigation," he said.
Engstrom, who was 52 at the time of the murder, was questioned as a witness early on in the investigation but police deemed him unreliable after he changed his story several times.
Media have suggested over the years that he was trying to cover up his role as the gunman. He died in 2000 at the age of 66.
Palme's son Marten told Swedish Radio he believed prosecutors made the right call.
"I think Engstrom is guilty. Given the current situation, I think it is reasonable to close the investigation," he said.
Another man was convicted of the crime in July 1989 after Palme's widow identified him in a widely-criticised line-up.
But Christer Pettersson -- a petty criminal and drug addict who shares no relation with the current chief prosecutor -- was freed months later by an appeals court which dismissed her testimony on a technicality.
Pettersson died in 2004, while Palme's widow passed away in 2018.
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