The 24-year-old pulled out after one rotation of the women’s team final on Tuesday in Tokyo, citing mental health concerns.
USA Gymnastics said Biles is yet to decide whether to withdraw from her four individual finals, which are scheduled to take place next week.
In a statement, USA Gymnastics said: “After further medical evaluation, Simone Biles has withdrawn from the final individual all-around competition.
“We wholeheartedly support Simone’s decision and applaud her bravery in prioritising her well-being. Her courage shows, yet again, why she is a role model for so many.”
Biles won four gold medals in Rio in 2016 and was aiming to become the first gymnast to retain a female all-around title at the Games since Vera Caslavska in 1968.
She successfully qualified for the final in first place but a mistake on her opening vault in Tuesday night’s team final prompted her to leave the arena with a US team medic.
Amid injury fears, Biles returned to the arena to support her team to an eventual silver medal behind the team representing the Russian Olympic Committee, and later revealed she had made her decision due to a desire to protect her mental health.
Biles said on Tuesday: “It’s been really stressful these Olympic Games, not having an audience. It’s been a long week, a long Olympic process, a long year. We are just a little bit too stressed out. We should be out here having fun.
“I feel like I’m also not having as much fun and this Olympic Games I wanted it to be for myself and it felt like I was still doing it for other people. It hurts my heart that doing what I love has been taken away from me to please other people.”