Governor Sultan al-Aradah was unhurt in the attack and there were no other casualties, it reported, citing an unnamed security source in the government-held Marib province.
The missile attack completely destroyed the governor's home and damaged several other adjoining houses in Wadi district in southeastern Marib, about 170 km northeast of the rebel-held capital Sanaa.
There were no comments from the Houthi group on the attack.
It was the second time the Houthi rebels used ballistic missile in its attack against neighboring province of Marib.
In September 2015, a Houthi ballistic missile attack on Marib killed 50 soldiers from the United Arab Emirates and Bahrain, which are part of the Saudi-led coalition forces supporting the Yemeni government in fighting against Iran-allied Shiite Houthi rebels since March 2015.