The Ministry of Defence website said Shehri was a Saudi national who was killed, along with six other militants, in any army operation in the remote Hadramout province in eastern Yemen. It gave no more details.
The United States has used unmanned drones to target AQAP, which has planned attacks on international targets including airliners and is described by Washington as the most dangerous wing of al Qaeda.
A Yemeni security source said Shehri was killed in an operation last Wednesday which was thought to have been carried out by a U.S. drone, rather than the Yemeni military. The source said another Saudi and an Iraqi national were among the others killed.
Shehri is a former inmate of the U.S. detention facility at Guantanamo Bay who was released to Saudi Arabia in 2007 and put through a Saudi rehabilitation programme for militants.
Yemen's government is trying to re-establish order after an uprising pushed out veteran ruler Ali Abdullah Saleh in February, but faces threats from Islamist militants, southern secessionists and a Shi'ite rebel movement in the north.
The protests and factional fighting have allowed al Qaeda's regional wing to seize swathes of south Yemen, and Shi'ite Muslim Houthi rebels to carve out their own domain in the north.
The lawlessness has alarmed the United States and Yemen's much bigger neighbour Saudi Arabia, the top world oil exporter, which view the impoverished state as a new front line in their war on al Qaeda and its affiliates.
Washington, which has pursued a campaign of assassination by drone and missile against suspected al Qaeda members, backed a military offensive in May to recapture areas of Abyan province.
But militants have struck back with a series of bombings and assassinations.
ADEN | Mon Sep 10, 2012 3:09pm BST
(Reporting by Dhuyazen Mukhashaf; Writing by Andrew Hammond; Editing by Alison Williams)