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The NGO's country director Shashwat Saraf told local media that the military had not given a reason for the closure.
"We are actually surprised that our Maiduguri office has been sealed off by soldiers. We have no idea why and have not been told," he said
Maiduguri, the Borno State capital, is the birthplace of the Boko Haram movement and has been repeatedly attacked by the group.
Six of the NGO's staff have been held in jihadist captivity since being seized by militants from the Islamic State West Africa Province (ISWAP) group in July.
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Their convoy was ambushed near the Niger border and their driver was killed.
According to the NGO, the staff featured in a hostage video released by ISWAP.
An AFP journalist outside the NGO headquarters on Thursday witnessed soldiers stationed by the premises.
"They came and asked everyone in the building to leave. They said it was an order from above," an NGO member said on condition of anonymity.
"We all evacuated the office (on Wednesday). They have been guarding the building since yesterday," the member told AFP.
At a press conference on Thursday, the Nigerian army made no mention of the incident.
It declined requests to comment.
Relations between the Nigerian and army and aid organisations in the region are tense, amidst a now decade-old insurgency and an ongoing humanitarian crisis.
Despite claims by the Nigerian government that Boko Haram has been technically defeated, the insurgency continues to rage, devastating the region.
More than 35,000 have died since the conflict began, with some two million people displaced and many reliant on food aid.