World Bulletin / News Desk
Fadl al-Jaadi came under fire as his car was passing near a military camp in Ad-Dali city.
The governor was unhurt in the attack, which injured two of his associates, the source said.
No group has yet claimed responsibility for the attack.
Al-Jaadi was appointed as Ad-Dali governor in mid-2015 by Yemeni President Abd Rabbuh Mansour Hadi.
Government forces control most of Ad-Dali province, while Houthi rebels rule some areas in the province.
Yemen fell into civil war in 2014, when Houthi rebels and allied forces of former President Ali Abdullah Saleh overran capital Sanaa and other parts of the country.
The conflict escalated in 2015 when Saudi Arabia and its Arab allies launched an extensive air campaign aimed at reversing Houthi military gains and shoring up Yemen’s Saudi-backed government.
UN-brokered peace talks between the government and Houthi rebels have failed to resolve the conflict, in which 10,000 people were killed and around three million displaced, according to UN estimates.