According to the local media, the Los Angeles Police confirmed the incident and said a 47-year-old Terry Bryant was arrested on Sunday over suspicion of felony grand theft.
McDormand had won the 'best actress' Academy Award for her performance in 'Three Billboards Outside Ebbing, Missouri'
The authorities have said the Oscar was allegedly stolen during the Governors Ball after party.
According to reports, Bryant had a ticket for the event.
Video captured by The Associated Press appears to show Bryant walking with the statuette out of the Governors Ball, the Oscars after-party where police say he took it.
The video shows a man in a tuxedo who appears to be Bryant holding an Oscar statuette highly and proudly as an onlooker cheers.
“All right baby boys, and baby girls,” he says, walking quickly and nearly bumping into a woman.
He then quickly glances around him before walking out of frame, prominently holding the Oscar the entire time.
Another photographer who took Bryant’s picture at about the same time did not recognize him as a winner at the ceremony, and began following him, police said.
When he was confronted, Bryant handed back the statuette without a fight, police said. He was detained by security guards at the event and arrested by Los Angeles police officers. The award was later returned to McDormand.
According to some reports, McDormand was spotted crying after giving up the search for the statuette on the premises and departing with her husband, filmmaker Joel Coen.
She was later reunited with the trophy.