Security forces in Yemen - the ancestral home of Osama bin Laden, the al-Qaeda leader - said they were looking for three other suspects.
A little-known group purportedly with al-Qaeda links claimed on Monday that it was behind the attack, launched allegedly in revenge for the slaying last year of Taliban military commander Mullah Dadullah in Afghanistan.
The Jund al-Yemen Brigades said in a statement, obtained by the Washington-based SITE group that monitors websites linked to extremist groups, their attack consisted of firing three mortar shells at the compound.
The statement's authenticity could not be independently verified.
Westerners were seen evacuating the compound after the explosions while security forces blanketed the area.
Troops were beefed up on roads leading to the US and British embassies.
Last month, mortar shells were fired at the US embassy in Sanaa but exploded instead at a nearby girls' school, killing a security guard and wounding more than a dozen students.
And in January, three Belgians and their Yemeni driver were killed during an attack in the country's east.
Meanwhile, in a deterioration of the security situation in the south of the country, a Yemeni soldier died after being wounded during a riot on Monday.
Yemeni security forces have been struggling to quell demonstrations by thousands of former southern army officers, political activists and unemployed men who have accused the government of unequal treatment.