It said a number of commanders were confirmed dead, naming them as Abubakar Mubi, Malam Nuhu and Malam Hamman, and said Shekau was "believed to be fatally wounded on his shoulders".
Sani Kukasheka Usman, a colonel and acting director of army public relations, described the strikes as "the most unprecedented and spectacular air raid".
He said the raid took place "while the terrorists were performing Friday rituals" at Taye village, Gombale general area within Sambisa forest, Borno State. "Several other terrorists were wounded," he said.
It is not the first time the Nigerian army has reported the death of Shekau, who led a break-away faction of Boko Haram when the main bulk of the group declared allegiance to Isis.