The closure has been imposed in Adamawa state, one of three states in the northeast placed under emergency rule in May following waves of attacks by Boko Haram Islamists.
The military has launched a major offensive in the area aimed at crushing the Islamist uprising, which has killed thousands since 2009.
Nigeria claims that the Islamists have set up bases in sparsely populated areas of its northeastern neighbours -- Cameroon, Chad and Niger -- and flee across the border after staging attacks to avoid military pursuit.
He said the measure had been in place since tomorrow and that it has already curtailed "the influx of miscreants (and) terrorist elements" into Nigeria.
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"Other security agencies like the customs, immigration services, have been told. Our soldiers and police are also there working together to ensure that nothing crosses into Nigeria," Nicholas said.
Despite the state of emergency, Boko Haram has continued to carry out attacks in the northeast, with more than 300 people killed already this year.
The full 2,000-kilometre porous border stretches from Borno down to the southern Niger Delta region.
Aside from curbing the flow of suspected insurgents, the several-hundred-kilometre closure in Adamawa will also affect traders and other residents.
Nicholas said the military was working with traditional rulers on both sides of the border to inform people about the closure.