The video, which was posted on January 5, is directly addressed to Cameroon's President Paul Biya after repeated fighting between militants and troops in the country's far north.
"Oh Paul Biya, if you don't stop this, your evil plot, you will taste what has befallen Nigeria... Your troops cannot do anything to us," Shekau said in Arabic.
Paul Biya has been mentioned by Shekau before but it is first time that he has directly addressed Cameroon and is the first admission that Boko Haram has been actively operating in the country.
The attacks have taken a similar form to those in Nigeria from hit-and-run raids to kidnappings.
Boko Haram, which began its violent insurgency in 2009, has taken over swathes of territory in three northeastern Nigerian states, and declared some towns as part of its Islamic caliphate.
Last weekend, fighters captured the key town of Baga and the headquarters of the Multinational Joint Task Force in the Lake Chad area, tightening its control of the remote state of Borno.
Biya personally ordered the air strike after the insurgents crossed the border and seized a military camp, the government said on December 29.
The aerial bombardment, hailed as a new phase in the counter-insurgency, forced the Islamists to flee, it added.
Shekau, in military fatigues and green rubber boots, speaks for more than 17 minutes in the video, flanked by four masked Boko Haram fighters, two of whom hold the militants' black flags.
There was no indication when the video -- entitled "Message to President Paul Biya of Cameroon" -- was shot or where.