“At this stage, we have not been made aware of any evidence of any credible threat to schools,” it said.
The police said the email originated from outside the UK.
PSNI Assistant Chief Constable Anthony McNally said: “We take incidents of this nature very seriously and we understand the concern in the community, school communities and for students and parents.
“Our enquiries are ongoing, however, at this stage we consider risk to the public as low.”
He added that the police “will continue to liaise with schools impacted”.
It is understood some schools have evacuated.
In October, a number of schools closed after an email threatened that “an explosive device” was located within hundreds of schools in Northern Ireland.
Police Scotland said “threatening messages were sent to a number of schools in Scotland and across and the UK”.
“These messages were immediately assessed and are being treated as hoaxes,” it said.
On Wednesday, An Garda Síochána (Irish police) said it was “aware of a generic communication that has been sent to a number of educational establishments”.
“An Garda Síochána assess this threat as not credible and is not advising any educational establishment to evacuate,” it said.
The EA said that “schools are advised to be vigilant and report any suspicious activity to PSNI”.
“We fully appreciate that any message of this nature is distressing and can assure schools, parents/carers and children and young people that we will provide a further update following engagement with police.”
Sinn Féin MLA Pat Sheehan said the “latest reports of sinister threats made to schools this morning are despicable”.
“It is completely unacceptable that school communities have once again been left facing this level of fear, uncertainty and disruption,” he said.
In a social media post, Alliance assembly member Paula Bradshaw condemned the “reckless bomb threats sent to schools this morning”.
“Such actions are unacceptable, causing fear and distress among pupils, parents and staff. Please remain calm and follow official guidance.”