Gabriel Aubry's claims are included in court papers that led a judge to grant a restraining order against actor Olivier Martinez, who is engaged to Oscar-winner Berry.
Aubry (37) was arrested on suspicion of misdemeanour battery after his confrontation with Martinez, but he states in the civil court filings that he was not the aggressor and that he was attacked without provocation.
Martinez told police that Aubry had attacked first.
Aubry's filing claims Martinez threatened him the day before the fight at an event at his daughter's school.
Aubry, a model, has a four-year-old daughter with Berry and the former couple have been engaged in a long custody battle.
The proceedings have been confidential, but Aubry states a major aspect of the case was Berry's wish to move to Paris and take her daughter with her.
The request was denied.
Aubry claims Martinez told him: "You cost us three million US dollars", while he was punched and kicked him in the driveway of Berry's Los Angeles home.
Aubry had gone to the home to allow his daughter to spend the Thanksgiving holiday with her mother, the filings state.
Aubry claims Martinez threatened to kill him if Aubry did not move to Paris.
Berry was not in the driveway during the confrontation and neither was their daughter, the documents state.
Photos of Aubry's face with cuts and a black eye were included in his court filing.
A judge set a hearing for December 17 to consider whether a three-year restraining order should be granted.
Aubry has a December 13 court date for the possible battery case, which has not yet been filed.