She has not decided on whether to participate in the balance beam final, which is scheduled for Tuesday. She earned bronze in the event in Brazil five years ago.
Biles had previously opted out of the all-around final, as well as the vault and uneven bars finals.
"Simone has withdrawn from the event final for floor and will make a decision on beam later this week," a tweet from USAG read. "Either way, we're all behind you, Simone."
Biles had qualified for all individual events last week and was the favorite to win multiple gold medals entering the Games. She had withdrawn from the team final on Tuesday, following the first event on vault.
She later told the media she had experienced "a little bit of the twisties" and no longer trusted her ability to compete. In a series of posts to her Instagram account on Friday, Biles explained she was still experiencing the phenomenon, in which gymnasts feel like they get lost in the air, and said her "mind and body are simply not in sync."
Biles will be replaced by Great Britain's Jennifer Gadirova in the floor final.
MyKayla Skinner said she believes Biles will compete in Tuesday's beam final, however.
"Yeah, I think so. I don't know for sure. It's kind of up to her. So that's the game plan," she said.
Biles was the reigning Olympic champion in the all-around, as well as on floor and vault. She is widely considered the greatest gymnast of all time.