The 18-year-old was knocked out when she fell on her face on the halfpipe on Sunday and was kept in hospital overnight for observation before being released on Monday.
"With a concussion injury there needs to be a rest period followed by a graduated return to play phase," Team GB doctor Niall Elliott said in a news release.
"The time scale is unfortunately too tight for Rowan."
Head coach Pat Sharples said the team were upset that Cheshire would not be able to compete in Thursday's competition but he was certain the Olympics had not seen the last of her.
"She is only 18-years-old and has a bright future ahead of her," he said. "I have no doubt she will back in four years time more determined than ever."