The officials said the bombs hit the men in their car while they were travelling on a coast road east of the Arabian Sea port of Mukalla, which was occupied by al Qaeda fighters in April after security forces retreated.
Al Qaeda in the Arabian Peninsula (AQAP) is the deadliest branch of the global militant organisation and has taken advantage of a war pitting Houthi militiamen against forces loyal to exiled President Abd-Rabbu Mansour Hadi to grab territory and operate more openly.
The chaos has also given rise to a Yemeni branch of the hardline Islamic State group, which on Tuesday claimed responsibility for a bomb planted near a police car in the capital Sanaa. No one was hurt in the blast.
Al Qaeda on Tuesday said it carried out 12 separate gun and bomb attacks on Houthi fighters in the central province on al-Bayda. It was immediately possible to confirm the claims.
The Houthis are a Shia Muslim sect and both al Qaeda and Islamic State consider the Iran-allied Houthis apostates.
The Houthis, who are fighting a Saudi-led coalition of Arab states, have advanced into many majority Sunni parts of the country since seizing the capital in September, in an advance it says is part of a campaign against the militants and a corrupt government.
Prior to the Houthi revolt, the US military was involved in the fight against the extremists but American personnel have since pulled out of the country.
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