The jihadist was said to have been wounded and one of his deputies killed when two air force jets bombarded fighters at Balla village.
The jihadist chief was said to have been wounded and one of his deputies killed when two air force jets bombarded fighters at Balla village, on the edge of the Sambisa Forest in Borno state, last Friday.
Surveillance footage showed missiles being fired on what the air force said were Boko Haram fighters, while the army announced it had "neutralised quite a number of terrorists", including in Balla.
"There were indications that quite a number of the terrorists' key leaders have either been killed or wounded," army spokesman Brigadier-General Sani Usman said earlier Thursday, without naming Shekau.
But in a 14-minute video, the shadowy Boko Haram leader claimed ignorance of both the incident and the location, insisting he was not injured and that none of his key lieutenants was harmed either.
"I'm alive, I'm alive, I'm alive," he said, wearing his trademark camouflage jacket and cradling an assault rifle.
"I'm alive, you have not killed any of my men. I didn't even know this incident you are talking about ever happened.
"What surprises me is your claim that I'm nursing wounds. Look at me well. Look at my sitting posture."
There was no indication where the video was shot.
In it, Shekau was flanked by two masked, armed men, sitting against what appeared to be a desert camouflage net and Boko Haram's black and white insignia.
He spoke in Hausa and Arabic.
The Nigerian authorities' reticence about naming Shekau is likely to come from previous occasions when his death has been announced prematurely, only for him to reappear in video messages.
He has rejected military claims the rebels are depleted and in disarray as a result of a sustained counter-offensive that began in early 2015 and recaptured swathes of territory.
A source with links to the Islamist militants told AFP on Wednesday that Shekau narrowly escaped death when the second missile hit as he was on his way to preach at Friday prayers.
"It's bloody propaganda," he said of Shekau's video denial.
"Shekau hurt his back from the impact of the second strike. He was injured in the back and then taken out of the area to a place around Kolofata (near the Cameroon border)," he added.
"You can see he is not the same Shekau we were seeing in other videos. He didn't exude the same energy."
The Boko Haram insurgency has left at least 20,000 people dead and made more than 2.6 million others homeless since 2009, devastating the region and leaving millions dependent on humanitarian aid.