Most of the affected schools are near Lake Chad and on the banks of the Yobe River, which marks the border between Niger and Nigeria, the UN's Office for the Coordination of Humanitarian Affairs said in a statement.
The agency said 151 schools with a total of 12,631 pupils had closed due to "insecurity that has sparked the absence of teachers and panic in the population".
"The pupils are now at camps for displaced people," the agency said, adding that there are no schools at the camps.
Thirteen people were killed and three injured in an attack on the Diffa village of Ala last week, local officials said.
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Niger's government has been working with the UN and other partners on a plan intended to allow children to go back to their studies in safer locations by the end of November.
Boko Haram has carried out a string of deadly attacks in Diffa, one of its strongholds on the Niger-Nigeria border, as the army struggles to contain the group's regional advances.
Boko Haram has been hit hard by the multinational offensive, losing territory, but it has launched attacks and bombings in response.