The Ministry of Defence website said Shehri was killed on Monday (local time), along with six other militants, in what it called a "qualitative operation" by the army in the remote Hadramout province in eastern Yemen. It gave no further details.
AQAP, which has planned attacks on international targets including airliners, is described by Washington, which has used unmanned drones to target its members, as the most dangerous wing of al-Qaeda.
There were conflicting reports on how Shehri, a former inmate of Guantanamo Bay, was killed. Yemen has previously announced Shehri's death only for it to emerge that he is still alive.
A Yemeni security source said Shehri was killed in an operation last Wednesday in the Hadramout which was thought to have been carried out by a US drone, rather than the Yemeni military. The source said another Saudi and an Iraqi national were among the others killed.
Residents of the Wadi al-Ain district where the attack took place last Wednesday said they believed from their contacts with Islamist fighters in the area that Shehri had died then, when missiles struck a house where they were meeting.
"There was a group of people from the Ansar al-Sharia group who were holding a meeting - Shehri was one of them and there were foreigners there too," said Elwi Suleiman. Ansar al-Sharia is one of a number of Yemeni militant groups linked to al-Qaeda.
There was no immediate explanation for the discrepancy in the accounts.
Shehri was released from the US detention facility to Saudi Arabia in 2007 and put through a Saudi rehabilitation programme for militants. He is wanted by Yemeni authorities for a suspected role in a U.S. embassy attack in 2008.
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.
A southern Yemeni politician who returned from exile survived an assassination attempt on Monday, a security source said. Last week 10 civilians were killed in an apparent drone attack that missed its target or was based on wrong information.
