Cipriani, 25, suffered a concussion Wednesday and multiple tests were carried out after he ran across a street Wednesday in Leeds, England, and was struck by a bus, the BBC reported Thursday.
James Williamson, Cipriani's agent, said the player is due to be released from the hospital Thursday. He said Cipriani is "quite groggy" and "does not remember much about the incident."
"At the moment there doesn't seem to have been any serious damage done. We don't how long he will be out for. It looks like he has been a lucky boy," Williamson said.
The incident took place while Cipriani and his teammates were on a pub crawl ahead of their season-ending match Sunday against the Wasps.
First Bus released a statement saying police have determined the company and its driver were not at fault in the incident.