"Over 300 terrorists were killed while a few were also captured," defence spokesman Chris Olukolade said in an emailed statement.
There was no independent verification of the claims, which follow similar assertions about Boko Haram casualties by Niger, Chad and Cameroon involved in the regional fight-back against the militants.
Civilian vigilantes in the town spoken to by AFP confirmed that the town had been retaken but said only that there were heavy casualties, without specifying numbers.
Monguno lies about about 125 kilometres north of Maiduguri, which has long been seen as a key prize for the militants in their quest to establish a hardline Islamic state.
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Olukolade claimed that the "massive" casualties came after a two-day operation to liberate Monguno and 10 other communities, which destroyed a cache of equipment, arms and ammunition.
The cache included five different types of armoured fighting vehicles, an anti-aircraft gun, some 50 cases of shells and eight different types of machine guns.
Two Nigerian soldiers were killed and 10 others injured in the operation, he said.
"The cordon and search operations is continuing along with aggressive patrols by troops who are now dominating the cleared communities," the statement said.
"The various phases of the highly coordinated air and land operations is also ongoing in the designated theatres being handled by contingents involved in the renewed counter-terrorism campaign in and outside Nigeria."
Nigeria's military has frequently made claims of successes against Boko Haram which have often been at odds with eye-witness accounts on the ground.