"The car has been returned but my nephew, Qaed Duaihan, is still being detained," he said.
In a posting on a website, the governor of Marib called on the three or four kidnappers to release the doctor to be released within the next few hours.
Kidnappings are common in Yemen, the world's poorest country, and hostages are usually freed unheard.
About 15 Yemeni Red Crescent workers were kidnapped and released in August.
But five Germans and a Briton captured in June are still missing, after the three others in the group kidnapped were found dead.
They were taken in Saada, another northern province, where the military is battling the so-called Houthi group, which is seeking to topple the government.