The Academy Award was said to have been taken at the Governors Ball party after the Hollywood ceremony.
Los Angeles Police Department said Terry Bryant, 47, had been arrested on suspicion of felony grand theft
He had a ticket for the ball and is being held in custody on $20,000 bail, an LAPD spokeswoman said.
McDormand received the Best Actress Oscar for her performance as a vengeance-seeking mother in Three Billboards Outside Ebbing, Missouri.
New York Times reporter Cara Buckley, who was at the Governors Ball, claimed a man had “grabbed” the award and “ran out with it”.
She said a photographer working for celebrity chef Wolfgang Puck stopped the alleged thief and seized the Oscar.
US media reported that McDormand was seen crying outside the ball after giving up the search for the statuette on the premises and leaving with her husband, filmmaker Joel Coen.
The actress has since been reunited with her award, according to reports.
It was the second time she had won the Best Actress Oscar following her win for Fargo 21 years earlier.
McDormand delivered a rallying cry for the #MeToo movement, which seeks to end harassment and gender double-standards, as she accepted her latest Oscar.
Placing her award on the stage, she asked all women nominated across each category to stand up and be counted.
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“Look around, ladies and gentlemen, because we all have stories to tell and projects we need financed,” McDormand said.
“Don’t talk to us about it at the parties tonight. Invite us into your office in a couple days, or you can come to ours – whichever suits you best – and we’ll tell you all about them.”