The vehicles hit explosives buried in the road, two government officials said. Muhammad Ali Maqdashi, the minister, remained unhurt.
At least six Yemeni soldiers were killed when a convoy carrying the country's defence minister was hit by a landmine explosion on Wednesday, but the minister was unharmed, government sources said.
Muhammad Ali Maqdashi, defence minister for the internationally-recognised government of Yemen, was visiting a frontline area of Sirwah. It is located west of the government-held city of Marib, and east of the capital Sanaa, controlled by the Houthi movement.
Six soldiers were killed and several others were wounded after the convoy hit explosives buried in the road, two government officials said.
Yemen has been mired in conflict since the Iran-aligned Houthis ousted the government of President Abd Rabbu Mansour Hadi from Sanaa in late 2014. A Saudi-led military coalition intervened in 2015 to restore Hadi.
Riyadh's intervention in Yemen triggered what the UN has called the world's worst humanitarian crisis.
Twenty-two million people in the country need aid, many of whom are at risk of famine.
Violence has flared along the front lines west of Marib city since mid-January, when a blast hit a government military camp in the area, killing dozens of people.
Landmines have been extensively planted in many parts of Yemen during the conflict.