St Teresa of Calcutta Catholic Academy Trust said emergency services were called after staff received the communication on 16 October.
All buildings at the school on Shaw Road were evacuated as a precaution, with children moved to a safe distance.
Greater Manchester Police confirmed the school had implemented a lockdown in response to the call.
A GMP spokesperson told Roch Valley Radio “Officers attended and carried out an assessment which indicated that the call was a likely hoax. Officers are investigating the circumstances of the call.”
The trust said specialist security operatives would carry out a full sweep of the building on Friday afternoon to establish whether further action was required.
Parents and carers were told they could collect their children or give permission for them to travel home.
In its statement, the trust said “All children and staff are safe and accounted for, in line with our established procedures.”
It said parents and carers had been notified immediately that children had been moved to safety and that there was no danger to anyone present.
One parent criticised the communication, saying they received an initial message through Arbor at 9.22am and the next update at 11.07am, with an email arriving later.
The parent said “Communication to parents was very poor.” They said they understood the situation but believed more updates should have been provided while parents were worried.
Roch Valley Radio approached the school office, headteacher and trust for comment during the morning. Calls to the school were subsequently met with a recorded message saying it was closed.
The trust also urged people to avoid speculation on social media, describing rumours about intruders or weapons on school premises as false.
It said further information would be provided following consultation with GMP and Rochdale Borough Council.
The school is currently expected to reopen as normal on Monday 19 October, with further updates to be issued if needed.
