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The Sale back was concussed and kept in hospital overnight to undergo X-rays, the club said, adding he was "on his way home (with) bumps and bruises."
Pictures in the British media showed Cipriani being treated by paramedics while lying on a stretcher in front of a bus, whose entire front widescreen was damaged in the incident late on Wednesday.
"A pedestrian suddenly ran into the road and collided with a First Bus travelling at a safe speed," a statement from the bus company read. "The police have investigated this incident and have reported that First and its driver are not at fault.
"We understand the pedestrian is an England rugby international, and we wish him a speedy recovery."
British media reported 25-year-old Cipriani was out with his Sale team-mates on a student pub crawl. He was wearing fancy dress.
Cipriani was widely considered the next big thing when he made a stunning international debut in 2008 but he fell out of favour with his national team in Martin Johnson's reign, with his form affected by fitness and off-the-field issues.
He recently returned to English club rugby after a spell with the Rebels in Australia.
