He issued a statement on Sunday saying: "I have agreed with Manchester United to take a period of absence while I address the allegations made against me.
"This was a mutual decision to avoid distraction to my teammates and unnecessary controversy for the club.
"I want to reiterate my innocence of the things I have been accused of, and I will fully co-operate with the police to help them reach the truth. I look forward to returning to play as soon as possible."
Antony has been accused of attacking his former girlfriend Gabriela Cavallin "with a headbutt" in a Manchester hotel room on 15 January, leaving her with a cut head that needed treatment by a doctor.
She alleges she was also punched in the chest, causing damage to a silicone breast implant, which required corrective surgery.
Antony previously said on social media about Cavallin's claims: "I can calmly state that the accusations are false and that the evidence already produced and the other evidence that will be produced demonstrate that I am innocent of the accusations made."
Ingrid Lana, a 33-year-old banker, has also claimed in a short clip released by Brazil's Record TV that she hit her head when "pushed against a wall" by Antony at his house in Manchester in October 2022.
Both Greater Manchester Police and Sao Paulo Police are looking into the claims.
Antony did not play in the international break after the Brazilian football federation said he had been withdrawn from their squad after "facts became public" that "need to be investigated".
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