United released a statement on Sunday to announce that Antony, 23, will delay his return to training "in order to address the allegations."
The decision was signed off by United chief executive Richard Arnold after talks with manager Erik ten Hag.
Claims have been made against Antony by three separate women, including his former partner Gabriela Cavallin. Antony, who was released from the Brazil squad on Monday following fresh accusations made by Cavallin, denies any wrongdoing.
United's statement read: "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.
"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."
A source has told ESPN that Antony, who has not been arrested or charged, has not been suspended and his time away is being described as a "leave of absence" to allow the forward to focus on defending himself.
He remains on full pay, and there is no timetable for his return. The claims made against Antony, who joined United from Ajax for £85m in 2022, are being investigated in Brazil and Manchester.
In a statement released by Antony on Sunday, he said: "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 cooperate with the police to help them reach the truth. I look forward to returning to play as soon as possible."