Boko Haram has staged numerous attacks across northern and central Nigeria, killing some 1,400 people.
The military has previously claimed to have arrested Abu Qaqa but this was denied by Boko Haram, who said the wrong man had been detained.
The joint military task force said it stopped a car suspected to be carrying some senior Boko Haram commanders in Kano, northern Nigeria.
A source close to the military said one of the people in the car tried to escape and was shot. He later died in the hospital.
The source said some of the people in the car have informed the military that the person shot was Abu Qaqa, the man who signs emails sent to the media on behalf of the group.
Analysts note that Abu Qaqa is an alias, so establishing his identity will not be easy.
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