ESPN Brazil confirmed earlier this week that Antony's ex-girlfriend, Gabriela Cavallin, filed a police report against him earlier this month, alleging four incidents of domestic violence, bodily injury and threat.
The complaint was filed at the 5th Women's Police Station, in the Tatuapé district of São Paulo. The investigation is ongoing.
Manchester United have not commented regarding the accusations.
Antony issued the statement following claims made by a 22-year-old woman in Brazil earlier this month.
Antony's statement read: "To friends, fans and followers. For you, after having given my testimony at the police station where the investigation involving my name is being conducted, I wanted to speak publicly, for the first time, since I was falsely accused of assault.
"I was silent so far so that nothing could interfere with the investigative process, but during all these days my family and I suffered in silence.
"Even though I was born and raised in a very needy community, I had never gone through a situation similar to this, in which a false accusation of aggression generated a previous and unfair public judgement on the part of some.
"After the closure of the investigation, my innocence will be proven, being certain that justice will prevail and the damage initially caused to my image will remain in the past. Thank you for the countless messages of support received at this very difficult time."
Antony, 23, joined United from Ajax in 2022 in a deal worth £85 million ($107.1m). He played 44 times in his first season at Old Trafford, scoring eight goals.