"To the despot Nigerian government: Die with envy. I'm not dead," Shekau says in the video.
An ISIS flag is visible in the background. That terrorist organization has said it is supporting Shekau's rival, Abu Musab al-Barnawi, as the legitimate leader of the Nigerian ISIS-affiliated terrorist movement.
The video was a response to the Nigerian army's claim that it "fatally wounded" Shekau in a raid August 19. The army dismissed the video Sunday as evidence of Shekau's desperation.
"The video has shown beyond all reasonable doubt the earlier suspicion that the purported factional terrorists' group leader is mentally sick and unstable," the army statement said.
CNN cannot independently confirm when the video was shot, or confirm its claims.
The attack that brought Boko Haram international notoriety was when Shekau's forces captured approximately 300 girls -- between the ages of 16 and 18 -- from a boarding school in the town of Chibok in Borno state in April 2014.
Boko Haram, which opposes western education, wants to set up an Islamic caliphate in Nigeria.
In the video, Shekau teases parents of the Chibok schoolgirls about whether their daughters will be released and insists detained Boko Haram fighters must be released for the return of the schoolgirls.
The kidnapping sparked global outrage and prompted global figures, including activist Malala Yousafzai and US first lady Michelle Obama, to support the campaign to #BringBackOurGirls.
For a year after they were taken, the abducted girls were kept together, Amina Ali, an escaped schoolgirl told CNN in August. Then some of the teenagers -- including her -- were "given" to the terrorists as wives.
Shekau, however, is still shrouded in mystery. A Boko Haram insider told CNN in August the group had split after new leader al-Barnawi broke with Shekau and left with some followers, a move which the insider said left Shekau with most of the fighters in the Sambisa forest and also in control of the schoolgirls, a powerful bargaining chip for the group.
The army contends Boko Haram is significantly weakened and has been "irrational and unreliable" in negotiations over the schoolgirls.