The Sale Sharks and former England fly-half was treated for concussion and underwent X-rays overnight, his club confirmed.
And Cipriani said on Twitter: "Out of hospital now. Once again, thank you for the messages. Thank you for all the well wishes, means a lot. My ribs are a bit sore. Feel like I've been hit by a bus..."
Newspaper reports claimed that 25-year-old Cipriani was on a night out with his Sale team-mates when the accident happened in the city's Woodhouse Lane area.
Sale, though, have not released any further information about events.
Cipriani was involved in a collision with a First Bus vehicle, and a spokesman for the company said: "A pedestrian suddenly ran into the road and collided with a First Bus travelling at a safe speed.
"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."
Pictures taken at the scene showed the bus had a shattered windscreen.
Cipriani, who has previously played for Wasps and the Melbourne Rebels, is nearing the end of his first season with Aviva Premiership club Sale.
Among well-wishers who tweeted him were footballer Michael Essien and Australian rugby union international James O'Connor, his former Rebels team-mate.
- Sports & Recreation