The posts are believed to have been directed at McAuley Catholic High School, which confirmed it was 'managing an incident' alongside South Yorkshire Police earlier today.
A police spokesman said: "We can confirm that police have received a report regarding potentially unauthorised and malicious posts made on a social media account.
"This information has now been passed to the North East Counter Terrorism Unit.
* Police 'managing incident' at Doncaster school "Enquiries to establish the origin of this content are underway and the circumstances will be fully investigated.
An update from the school, based in Cantley Lane, Cantley, released this afternoon said: "The matter that has been reported is currently being investigated by the Police. At this time pupils and parents are advised to not reply to any unsolicited emails or social media and to report anything of concern to the School/Police.
"A continued Police presence will be provided whilst the investigation continues and a Specialist Officer will be in school tomorrow should advice be required.
"At this time both the School and Local Authority, together with the Police see no reason to advise pupils to remain away from school and there is no information that would require the school to close."