Nottinghamshire Police confirmed it was aware of the issue.
A spokesman said: “As a precautionary measure, we will have a heightened presence in several areas over the next few days, which will include reassurance patrols at schools.
“We are in close contact with schools and we are working with partners and other interested parties, while carrying out intelligence checks.
“We will not tolerate violence and any incidents reported to us will be investigated accordingly.
“Anyone involved in incidents of violence and disorder will be robustly dealt with.”
Leicestershire Police said: “Those schools referenced in the post have been contacted by officers from their relevant Neighbourhood Policing Area (NPA) and advised to report any issues or concerns.
“An appropriate policing plan is in place.”
Sharing the school warning letter, Broxtowe councillor Richard MacRae said it was “not good when a local school is having to send out such an email”.
Neil O’Brien, MP for Harborough, Oadby and Wigston, posted on social media that he had been contacted by “many worried parents”.
“I’ve written to the chief constable of Leicestershire Police today asking what action is being taken to stop this and to reassure parents, teachers and pupils.
“This is exactly the kind of problem that shows why I have been pushing for a social media ban for under-16s.”