A defense official said Bama, deputy to Boko Haram leader Abubakar Shekau, died in the community of Bama, in the northeastern state of Borno, the Lagos-based newspaper The Guardian reported Wednesday.
Spokesman Brig. Gen. Chris Olukolade described Bama as a specialist in manning anti-aircraft guns. Nigeria had offered a $155,000 reward for his capture.
Bama's father, Abatcha Flatari, who Olukolade said was one of Boko Haram's "spiritual guiding lights," also was killed in fighting.
Some 24 insurgents were arrested, the spokesman said. They confirmed Bama's death.
The clash came during a period of emergency rule imposed on Borno and two other northern states by the federal government in an attempt to quell Boko Haram violence.
Following a recently deadly attack by insurgents on a mosque, Muslim leaders have expressed doubts about the effective of the emergency declaration.
Muhammad Abubakar Sa'ad III, the Sultan of Sokoto and leader of the Muslim faith in Nigeria, said in a statement Wednesday "with the visible security checkpoints at every nook and cranny of the state, it is hardly believable that such dastardly acts could still occur unabated."
He said restoration of satellite-based telephone service to "selected/strategic government officials" should be a top priority to improve security.