The American left the arena after the vault, but later returned to support her team-mates as they claimed silver behind the Russian Olympic Committee.
Biles, 24, scored 13.766 - her lowest Olympic vault score - before withdrawing from the event.
"After the performance I did, I just didn't want to go on," she said.
"I have to focus on my mental health. I just think mental health is more prevalent in sports right now.
"We have to protect our minds and our bodies and not just go out and do what the world wants us to do.