The strikes hit positions west of Bayda and near the rebel-controlled town of Jaar, officials said.
Local sources claimed the attacks in the Bayda area were carried out by US drones or warplanes, but there has been no independent confirmation.
Local officials said Yemen air force planes carried out strikes on Saturday near Jaar.
Officials in Bayda said Friday night's raids targeted a stronghold of local al-Qaeda leader Abdulwahhab al-Homaiqani. He was among the dead, a government source told Reuters.
One official told AFP the dead were mostly, "new recruits, youths from the region, taken by surprise by the raids which struck as they were dining in training camps".
The militants were reported to have equipment, weapons and vehicles in order to carry out attacks.
Local residents in both Jaar and Bayda told Reuters the strikes were aimed at Ansar al-Sharia, a group linked to al-Qaeda in the Arabian Peninsula (AQAP).
Little detail has been given about Saturday's strikes on targets near Jaar, some 12km (7 miles) from the provincial capital Zinjibar, which is also in the hands of rebels.
Reuters quoted an Ansar al-Sharia spokesman as saying nobody was killed in the strike on Jaar.
AQAP is known to have bases in southern Yemen, and has been targeted in air strikes by unmanned US drones in the past.
Militants believed to be linked to al-Qaeda have exploited a security vacuum in the region after months of protests demanding the resignation of long-time president Ali Abdullah Saleh.
Friday's strike comes weeks after Abdrabbuh Mansour Hadi was sworn in as president, and suggests a new determination against the fight against al-Qaeda in Yemen, BBC Middle East correspondent Jon Leyne reports.
Such a drive would most likely be in collaboration with the US, which has recently talked about restarting a major programme of assistance, our correspondent says.