The teenager fell on her face at the Extreme Park halfpipe on Sunday and was knocked unconscious for several minutes before being carried away on a stretcher in a neck brace.
"Cheshire will be discharged today after the doctors were happy with her progress," said a Team GB statement.
"She will return to the athlete's Mountain Village where she will be looked after by team medical staff.
"Her progress will be monitored on a day to day basis as is standard with concussion and a determination regarding her ability to compete will be made later this week."
Cheshire posted a picture of her bloodied face on Twitter (twitter.com/Rowan_C_) along with the message: "Wasn't the best day yesterday, still don't remember much! Thanks everyone for the lovely messages."
The 18-year-old was considered an outside chance of a medal at the Sochi Games after becoming the first British woman to win halfpipe gold at a World Cup event in Calgary in January.
The women's halfpipe takes place on Thursday.
- Sports & Recreation