In a tweet from its official account, the army said there had been heavy casualties and that "mopping up" operations were continuing.
The Nigerian army's claim is yet to be independently verified and no further details have been released.
Nigeria says 150 people died when Boko Haram took Baga and nearby Doron Baga, but locals said up to 2,000 died.
Nigeria, Chad, Cameroon and Niger recently formed a military coalition against the Islamist militants.
Boko Haram controls of much of Nigeria's north-east.
The Nigerian army has been criticised by its failure to tackle the militant group, although it has recaptured some territory in recent weeks.
Last week, Nigeria retook the north-eastern towns of Monguno and Marte from the group.
The massacre at Baga is considered to be the worst attack of Boko Haram's six year insurgency.
Thousands fled across Lake Chad when the assault began and have since taken refuge in Chad.
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