"We take internet bullying and harassment seriously, it doesn't matter if it's a teacher or a pupil who is being insulted," the school's principal, who did not appear by name, told the local newspaper Stavanger Aftenblad.
The schools says their report concerns one isolated incident.
"We have a zero tolerance police towards bullying, and people can just post whatever they want."
Bjarne R. Birkeland i Stavanger, head of schools in Stavanger municipality, also weighed in on the matter, saying that local lawmakers were taking the incident seriously.
"It is important to report serious incidents to send a a signal about what is OK and what is not OK," he told the NTB news agency.
"It's all the most serious when things start sounding threatening, then it very clearly crosses the line," said Birkeland, without commenting further on the nature of the suspected harassment on Facebook.
He said that social media bullying was still rare, but that a few cases did pop up in his school district every year. The municipality itself can chose to suspend a pupil for three days maximum.
"This is about the right to a good working environment, for students and staff. The consequences of bullying at work are well documented," Birkeland said.