The unmanned aircraft struck a vehicle in Bayhan district, on the border between Shabwa and Marib provinces, killing two people on board, the official said.
On Sunday, elite US forces launched a dawn raid some 60 kilometres (40 miles) northwest of Bayhan, the first major US military operation against jihadists in Yemen since President Donald Trump took office on January 20.
At least 14 suspected members of Al-Qaeda in the Arabian Peninsula (AQAP) were killed in the attack, while one American soldier was killed and four others wounded, the US military said.
A Yemeni provincial official gave a higher toll of 41 presumed militants and 16 civilians killed in the raid, including eight women and eight children.
Although the US only sporadically reports on its long-running bombing campaign against AQAP, it is the only force known to operate armed drones over Yemen.
Al-Qaeda and the Islamic State jihadist group have exploited a power vacuum created by the two-year-old conflict in Yemen between the government and Shiite Huthi rebels, especially in the country's south and southeast.