It happened as the tourists passed a vehicle at the entrance to Mahram Bilqis, an ancient oval-shaped temple celebrated for belonging to the Queen of Sheba, an official said.
Meanwhile, Yemeni authorities arrested 12 people suspected of links to the blast, a security official told the Associated Press on Monday.
The official said those detained are members of a group believed to have information on the actual perpetrators of the attack.
No group has claimed responsibility for the explosion.
Khaled al-Hammadi, a journalist in Yemen's capital, Sanaa, told Al Jazeera that the attack took place amid a government crackdown on al-Qaeda in the country.
"The Yemeni government has conducted a lot of operations to combat al-Qaeda's operations in the country with the co-operation of the international community, particularly the US government.
"There are currently a lot of [court] trials in which al-Qaeda members are accused," he said.