It has been claimed it was issued by the Red Hand Defenders on Friday.
The PSNI said they are aware of the threat and are looking into it. They urged local community leaders to play "an active role in diffusing tension".
A statement continued: "Police are aware of a threat that has been made in relation to a number of schools in north Belfast.
"The threat was made through a third party on Friday 6 September 2013. Investigations into the threat are ongoing. At this stage there is no evidence to corroborate the threat.
"Police are committed to protecting all communities in North Belfast and we would encourage all community leaders and those in positions of influence to play an active role in diffusing tension and maintaining calm."
Gerry Kelly of Sinn Féin has condemned the threat.
"This is a disgraceful and sinister statement to come from any organisation or individual against school children, their parents and teachers," the North Belfast MLA said.
"Those responsible have threatened violent action against children.
"We must now see unionist and loyalist leaders coming out and condemning these threats in the strongest possible terms, call on the Red Hand Defenders to withdraw this threat and actively support the rights of any child to attend any school of their choice where ever it may be situated and receive their education with without fear or intimidation."