Aubry, who is the father of a 4-year-old daughter Nahla with Berry, was apprehended and subsequently admitted to hospital on Thanksgiving morning (Thursday, November 22), TMZ claims.
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Sources told the website that when Aubry dropped Nahla off at Berry's home on Thursday, the actress's current partner Martinez reportedly told him, "We have to move on".
The pair are then alleged to have become involved in a fist-fight and struggle, with Berry apparently rushing the child inside the house.
Aubry's reported injuries include a broken rib and bruises to his face. He may have suffered an additional, more serious head injury, and there are conflicting reports about whether he was left unconscious after the fight.
The model has since received treatment at a Los Angeles hospital, and is reported to have been formally booked on suspicion of misdemeanor battery with bail set at $20,000 (£12,539).
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Aubry is thought to have been released from police custody on Thursday evening.
Martinez is alleged to have suffered injuries including a possible broken hand. He is believed to have been treated at the same hospital as Aubry, but around an hour later.
According to law enforcement sources, an emergency protective order has also been issued which will require Aubry to stay a minimum of 100 yards away from his daughter, Berry and Martinez.
An LAPD spokesperson for the force's Hollywood division confirmed to Us Weekly that an investigation is underway, and that "the cause of the fight between the two men is unknown".
