Terry Bryant, 47, was arrested on suspicion of felony grand theft, said Officer Rosario Herrera, a police spokeswoman.
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.
“After some brief time apart, Frances and her Oscar were happily reunited. They celebrated the reunion with a double cheeseburger from In-N-Out Burger,” McDormand’s publicist, Simon Halls, told the AP.