St Edmund Arrowsmith Catholic High urged parents to “please reinforce our message in school that pupils must sit in a seat for their journey if they choose to use the top deck of a bus”.
The school said it was in contact with the boys’ families “to offer our support” and was also offering support to pupils who witnessed the incident.
In a statement, the school head teacher, Mark Dumican, said: “Contrary to some reports, there are no life-threatening injuries, and all three boys have been assessed in hospital.
“We are working with the police and with Vision Bus Company to determine the circumstances that led to this incident.”
Greater Manchester Police earlier said the incident appeared “to be an unfortunate accident”.
The BBC has also contacted Vision Bus Company for comment.