A Yemeni soldier also died and another was wounded when troops stormed the residence of an alleged insurgent identified as Abdullah Hubaibat, on the outskirts of the town of Loder, the officials said.
Two other jihadist suspects were wounded in the firefight and a third was arrested, the sources told AFP.
Government forces backed by a Saudi-led coalition entered Abyan’s capital Zinjibar last month and have recaptured other towns across the province.
The Arab coalition battling Iran-backed Shiite Huthi rebels in Yemen has also been providing government troops with air cover throughout their war against Al-Qaeda and the Islamic State group.
The United States has carried out numerous drone strikes against Al-Qaeda in the Arabian Peninsula (AQAP) operatives in Yemen.
In other unrest, an army colonel and four soldiers have been killed and 19 wounded in clashes with the rebels since Sunday on the frontier between Lahj and Taez provinces in southwest Yemen, a military official said Monday.
Taez province is mostly controlled by the rebels and their allies, while Lahj is one of five southern provinces that coalition-backed government forces recaptured over the summer.
The coalition began its military campaign in March 2015 against the rebels after they closed in on President Abed-Rabbou Mansour Hadi in his refuge in the southern port city of Aden.
More than 6,600 people have been killed since the coalition launched its intervention, most of them civilians, and at least three million people have been displaced, according to the United Nations.