Jara's family filed the civil lawsuit in Jacksonville, Fla., against Pedro Barrientos, one of eight former Chilean army officers charged last year in the singer's death.
Barrientos has lived in Florida for more than two decades, CNN reported Thursday.
The lawsuit, filed Wednesday, alleges Barrientos executed Jara in a game of Russian roulette 40 years ago, then ordered his subordinates to fire into the corpse.
The family seeks compensatory and punitive damages.
Barrientos, who denied the accusations, has not been arrested since being charged in Chile.
Jara, a member of the Communist Party and cultural ambassador for socialist President Salvador Allende, was arrested immediately after the September 1973 military coup. His body, which showed signs of torture and had 44 bullet wounds, was found a few days later in a field.
The 26-page lawsuit, which details brutality carried out during the coup led by Gen. Augusto Pinochet Ugarte, was filed eight months after Chilean authorities indicted Barrientos for Jara's murder, the Orlando Sentinel reported.
Chile's Supreme Court has granted a request for Barrientos' extradition from the United States, but it hasn't been submitted formally to U.S. officials, the Sentinel said.
The lawsuit says Barrientos moved to the United States in 1989 and lived in Winter Springs, Longwood and Deltona. The Sentinel said it was unsuccessful in trying to reach Barrientos.