Receiving award from Jennifer Lawrence and Jodie Foster, Frances said in her acceptance speech, "I'm hyperventilating a little bit. They also celebrated their reunion with a double cheeseburger from In-N-Out", McDormand's representative told the press.
The statuette has since been returned to the best actress victor. Security at the event was notified and detained Bryant.
He quickly gave it up when confronted by a photographer, police say. However, the thief has since been arrested by the Los Angeles police.
Once the women who had been nominated for awards at the event were on their feet, McDormand addressed the rest of the room.
In "Three Billboards", McDormand played Mildred Hayes, a hardened woman seeking justice for her daughter's murder in the crime drama.
It's the second time Frances has bagged an Academy Award, 21 years after her first for "Fargo".
Bryant was arrested near midnight for grand theft with $20,000 bail.
The account appears to show Bryant at several awards shows and movie premieres, including the Golden Globes and the Grammy Awards, and shows him posing alongside several celebrities including Selena Gomez, Jimmy Kimmel and Mariah Carey.
Bryant is accused of swiping McDormand's Oscar statuette from the black-tie Governor's Ball where Oscar winners have their awards engraved. "This is mine. We got it tonight, baby". "This is mine", he said, before planting a kiss on the Oscar's head.
"I lost my Oscar", the two-time Oscar victor said, shrugging her shoulders as she left the party, according to video recorded by Reuters Television. If I fall over, pick me up because I've got some things to say.