Fields, the 28-year-old defending gold medalist in men's BMX racing, suffered a brain hemorrhage after the wreck during the race semifinals, USA Cycling officials said in a statement.
"After a night in the ICU, the doctors are pleased to report that there has been no additional bleeding, and no new injuries were found," the statement continued. "Fields has been moved out of the critical care unit and will remain in the hospital until cleared."
"The staff has been in contact with his immediate family as they have navigated his care options after evaluation," officials said.
Fields' father told USA Today that he also broke a rib and bruised his lung in the accident and that the family hoped he would leave the hospital within five days and be flown home.
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"There's a bit of fluid on his brain, but it has not increased for the next 24 hours, so they're feeling good about that,'' Fields' dad, Mike, said. "So far the results seem pretty positive."
"Cognitively, he's doing well," Mike told USA Today of his son. "He knows where he is. He knows his birthday. He recognizes people.''
Mike also praised the "extremely good care" for him in Tokyo.
Fields had been a favorite for the podium after a strong showing in the quarterfinal on Thursday.
Video from Friday appears to show the front wheel of Fields' bike clip the race leader as they head into the first turn, causing him to tumble forward on his head as he is pummeled by racers behind him.
Photo by Ezra Shaw/Getty Images
"I just hope he's okay, I think he's been a great ambassador for the sport," Netherlands' Niek Kimmann, who won gold, told reporters afterward.
Kimmann added: "For me it's sad he wasn't able to defend his gold medal ... I can't wait to medal with Connor again soon."
To learn more about Team USA, visit TeamUSA.org. Watch the Tokyo Olympics now on NBC.