Instead, an unidentified young man speaks in the name of “The army of the caliphate in West Africa”.
Mr Shekau’s absence from the video has fuelled speculation about his fate.
In the 10-minute video, the speaker dismisses as a lie the Nigerian military’s assertion that it has recaptured all cities and towns from the militants.
He shows the identity cards of government troops he says have been killed, and the wreckage of what he describes as a jet that had been brought down.
BBC Nigeria analyst Naziru Mikailu says the video appears to be a genuine Boko Haram production.
The fact that it was issued under the banner of “The army of the caliphate in West Africa” reflects that the group is now allied with Islamic State (IS) militants fighting for a global caliphate, he says.
The speaker, who was carrying a rifle and whose face was covered, said the video was shot in Sambisa, a vast forest surrounding a game reserve. The group controlled the forest, and was running education projects – ranging from studies about Islam to technology – for people under its rule, he said.
Speaking in Hausa, he said:
“The armies claim through the media that they captured our towns and that they assaulted Sambisa (forest) and defeated us,” he said, referring to the bushland area in Nigeria’s northeast Borno state that has been an Islamist stronghold.”
“I swear by Allah that I am talking right now from Sambisa. Here in Sambisa you can travel more than four to five hours under the black flag of Islam by car or by motorbike. We are uncountable in Sambisa. We are thousands of Mujahedeen here.”
However, Mr Shekau’s absence from the video, and the failure to mention him, is surprising, our correspondent adds.
It suggests a split in Boko Haram or one of three other possibilities:
Mr Shekau has been wounded
He has been killed or
He has gone deep into hiding, making it difficult for him to appear in the video.