Government sources say the minister, Mohammed Nasir Ahmad, was unharmed in Tuesday's blast near government headquarters in the capital, Sana'a.
At least five of the minister's bodyguards were among those killed.
There was no immediate claim of responsibility.
The attack came a day after authorities announced that the second-in-command of al-Qaida's Yemen network had been killed in an army operation.
The Yemeni Defense Ministry said Monday that Said al-Shehri, a Saudi national, was one of several militants killed in an operation in Hadramout province.
Al-Qaida's Yemen-based network, al-Qaida in the Arabian Peninsula, remains active in southern Yemen. Suspected militants have carried out suicide bombings and have targeted Yemeni government officials for assassination.