The player's former girlfriend Gabriela Cavallin brought forward fresh charges of abuse against the forward last week.
Two more women have since come out with abuse allegations against the former Ajax Amsterdam forward.
The 23-year-old was dropped from the Brazil squad for their FIFA World Cup qualifiers against Bolivia and Peru as a result.
A club 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 statement from Anthony read: "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 team-mates 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."
Last month, the Old Trafford club were forced to cut ties with academy graduate Mason Greenwood following an internal investigation into allegations of domestic abuse on his partner.
Greenwood has since joined Spanish La Liga side Getafe on a season-long loan.
