The 23-year-old player earlier this week was dropped from the Brazil squad after accusations of physical aggression on several occasions since January towards his former girlfriend Gabriela Cavallin, which are being investigated by police and which he denies.
Antony was due back to training on Monday, but United have agreed with the player for him to stay away from the club in order to focus on defending himself.
Antony has not been arrested or charged and says he will co-operate with police in order to prove his innocence.
United, fresh from dealing with Mason Greenwood's exit from the club, said in a statement: "Manchester United acknowledges the allegations made against Antony.
"Players who have not participated in international matches are due back in training on Monday. However, it has been agreed with Antony that he will delay his return until further notice in order to address the allegations."
United, who have not suspended Antony, will continue to monitor the situation as it develops, with manager Erik ten Hag consulted on the decision.
United added: "As a club we condemn acts of violence and abuse. We recognise the importance of safeguarding all those involved in this situation, and acknowledge the impact these allegations have on survivors of abuse."
Antony will remain on full pay and hopes to return to the club as soon as possible.
"I have agreed with Manchester United to take a period of absence while I address the allegations made against me," he said in a statement.
"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 cooperate with the police to help them reach the truth. I look forward to returning to play as soon as possible."
(With AP inputs)