The bombers, in explosives laden cars, tried to attack an oil refinery in Maarib, a lawless tribal area in the desert east of the capital Sanaa and a Canadian-run terminal in the southeastern port of Dhabba on the Gulf of Aden.
"The two attempts, at around 5:30 am local time (0230 GMT), were foiled by the forces in charge of security at oil installations and the Yemeni army," a security source said.
"In Maarib, the two booby-trapped cars exploded before reaching their target after coming under fire from security forces and soldiers. The two assailants were killed," he said.
At the Dhabba oil terminal, believed to be operated by a Canadian company, the bombers' two cars also exploded outside the site and the attackers were killed, along with a guard who was hit by gunfire.
The attack came just days after Osama bin Laden's right-hand man Ayman al-Zawahiri warned that the Gulf and Israel would be the next targets of Al-Qaeda, in a video message coinciding with the fifth anniversary Monday of the September 11 attacks on the United States.
It also followed an attempt by Islamic extremist gunmen to storm the US embassy in Damascus on Tuesday that left four attackers and a guard dead.
Tribesmen also abducted four French tourists in southeast Yemen Sunday in a bid to put pressure on authorities to free jailed members of their tribe.