Ali Abdullah al-Saleh, Yemen's president, said on Tuesday he would form a panel to investigate the air raid. Yemen's supreme security committee also issued a statement apologising for the botched attack.
Al-Shabwani was reportedly travelling to meet an alleged member of al-Qaeda in the Arabian Peninsula, the al-Qaeda offshoot in Yemen.
"The deputy governor was on a mediation mission to persuade al-Qaeda elements to hand themselves over to the authorities," a local government official said.
Tribal sources told Al Jazeera that the attack took place in Wadi Abida in the al-Shabwan district of Maarib.
The target of the attack, Mohamed Said bin Jardan, was reportedly wounded but managed to escape, according to Yemeni security services.
The area has witnessed several US drone attacks against suspected al-Qaeda fugitives over the past four months.
Members of al-Shabwani's tribe responded to his killing by attacking the pipeline that carries oil from Maarib to Ras Isa, a terminal on the Red Sea coast.
Shipping companies said the attack would not disrupt oil exports from Ras Isa, which refines roughly 30,000 barrels per day.
Tribesmen also tried to occupy the presidential palace in Maarib, but they were repulsed by Yemeni soldiers and army tanks. Local government offices have been shut down throughout the province.