Military officials say commander Momodu Bama died in a gunbattle earlier this month in the country's northern region.
There has been no confirmation of the commander's death from the militant group.
On Monday, a new video emerged by Boko Haram's self-declared leader, Abubaker Shekau.
He claimed responsibility for several recent attacks and urged Nigerians to abandon the country's constitution and accept Islamic law.
The group has been fighting to impose a strict form of Sharia on the country's Muslim-majority north.
Boko Haram has been blamed for thousands of deaths since it launched an uprising against the government in 2009.
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