Gabriela Cavallin had previously filed a police report in Sao Paulo, Brazil, accusing the players of 'domestic violence, threat and bodily injury'.
Antony had allegedly assaulted 22-year-old Cavallin on May 20, the same day Man United defeated Bournemouth 1-0 in the Premier League.
The Man United forward has since taken to Instagram to shed light on the siutation.
"To friends, fans and followers. For you, after having given my testimony 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," he wrote.
"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.
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"Even though he was born and raised in a very needy community, he 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."
The 23-year-old Brazil international joined United from Ajax in an £87m move last year.
He scored ten goals in 47 appearances in his first season.