The source said 14 Shiite rebels were also killed over the past 24 hours in intense fighting for Sarwah, the last district in the mainly Sunni province still held by the rebels.
The government has been battling since last year to retake the mountainous district which commands the main road to the capital Sanaa.
Despite the military intervention of a Saudi-led coalition in March 2015, the government's writ is still largely confined to the south and areas along the Saudi border.
Both Hadramawt and Shabwa have seen significant activity by Al-Qaeda, which has taken advantage of the conflict between the government and the rebels to expand its presence.
The World Health Organization estimates that more than 8,000 people have been killed in the conflict, most of them civilians.
The country has also been hit by a deadly cholera outbreak and faces the risk of famine.