He said the vehicle was blown up in Manaseh, a village in the province, leaving at least four Houthi rebels dead.
Other Houthi rebels were injured in the blast, the source, speaking on condition of anonymity, told The Anadolu Agency.
He said armed tribesmen and Houthi rebels continued to fight on the village's outskirts.
AA could not obtain immediate comment from the Houthi leadership regarding Tuesday's attack.
For the last several months, Yemen's Shiite Houthi group – which boasts thousands of diehard supporters – has been trying to step up its armed presence across the fractious country.
The Houthi movement has recently emerged as a political and military power in Yemen after taking over Sanaa and seeking to extend its influence into other provinces.
The Houthis' growing power has pitted the group against Sunni tribes and Al-Qaeda, the latter of which is said to still be active in certain parts of the country.
The recent ascendance of the Shiite Houthis has also caused concern in predominantly Sunni-Muslim Gulf States.