A woman, thought to be a former girlfriend of the Brazilian, is reported to have accused the 23-year-old of assaulting her on a number of occasions, including at least one incident in England.
Antony, who moved to Old Trafford from Ajax last summer, has revealed that he has now spoken to police about the situation and has vowed to clear his name after the investigation.
"To friends, fans and followers. For you, after submitting my statement at the police station where the investigation of the investigation involving my name is being conducted, I wanted to speak publicly for the first time since I was falsely accused of assault," Antony posted on his official Instagram account.
"I stayed silent until the moment so that nothing could interfere with the investigation process, but during all those days my family and I suffered in silence.
"Despite being born and raised in a very needy community, I had never been through a situation similar to this, in which a false assault charge resulted in a preliminary and unfair public judgement on the part of some.
"After the closure of the investigation my innocence will be proven certain that justice will prevail and the damage initially caused to my image will be in the past.
"Thank you for the countless messages of support received at this very difficult time."
Antony was a regular for Man United during his first season at the club, featuring on 44 occasions in all competitions, contributing eight goals and three assists in the process.
The Brazil international missed the end of the campaign, though, due to an injury that he suffered against Chelsea in the Premier League on May 25.
Antony was believed to have had a chance of being involved in the FA Cup final against Manchester City, but he was ultimately left out of the squad for what proved to be a 1-0 loss for Erik ten Hag's side.
The forward is set to link up with his teammates next month for pre-season, with Man United beginning their preparations for the 2023-24 campaign with a friendly against Leeds United on July 12.