The player's former girlfriend Gabriela Cavallin has brought forward fresh charges of abuse against the forward this week.
Greater Manchester Police are conducting an investigation into the matter but Antony has denied any wrongdoing.
The 23-year-old has been dropped from the Brazil squad for their upcoming FIFA World Cup qualifiers against Bolivia and Peru as a result.
In a statement on Wednesday, the club said: “Manchester United acknowledges the allegations made against Antony and notes that the police are conducting enquiries.
"Pending further information, the club will be making no further comments. As a club, we are taking this matter seriously, with consideration of the impact of these allegations and subsequent reporting will have on survivors of abuse.”
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.
