The children had been tending a herd of goats on a mountain outside the village of Yakla, in Baida province, when the strike hit on Sunday, the official said.
There was no immediate comment from the Pentagon.
The US has conducted more than 40 strikes against Al-Qaeda in Yemen since stepping up its air war against the jihadists on Thursday.
The Pentagon has said that none of the strikes have been conducted based on intelligence gathered in a botched US raid in January, the first authorised by President Donald Trump, in which multiple civilians and a Navy SEAL were killed.
Washington regards Al-Qaeda's Yemen-based branch, Al-Qaeda in the Arabian Peninsula (AQAP), as the jihadist network's most dangerous and says it has been plotting attacks on the West in recent months.