Six people were injured when the roof of a double-decker bus was ripped off as it hit a railway bridge.
Emergency services were called to the scene in Heaton Norris, Stockport, at about 1.40pm on Saturday.
Ten passengers were on the TransPeak bus at the time of the collision in Georges Road.
One man was briefly trapped on the top deck before he was rescued by firefighters, said police.
Three women and three men were taken to hospital for treatment to cuts and bruises.
The bus driver was not injured.
Sgt Danny Byrne, from Greater Manchester Police's Serious Collision Investigation Unit, said: "It is only by sheer luck that no-one was seriously injured.
"If you were in the area at the time of the crash and witnessed the incident I would urge you to contact the police with any information."
Anyone with information should GMP's Serious Collision Investigation Unit on 0161 856 4742 or the independent charity Crimestoppers, anonymously, on 0800 555 111.