"Three policemen were killed and six others were wounded in a suicide attack on a checkpoint in Suwadeya," the official said.
After the attack, carried out with a bomb-laden vehicle, clashes broke out between extremists and security forces in which the province's Al-Qaeda chief, Naser al-Dhafri, and another militant were killed, the source said.
Dhafri was the "mastermind" behind Tuesday's attack, the source added.
The official said the extremists managed to capture two policemen.
Air strikes also targeted Al-Qaeda positions, including a suspected training camp, in neighbouring Abyan province, where a March 4 attack on an army camp killed 185 soldiers.
"Yemeni air forces launched six raids on Tuesday against Al-Qaeda posts in Jaar," an Al-Qaeda stronghold in Abyan, said a military official.
"Three raids targeted an Al-Qaeda weapons hideout and a training camp west of Jaar," and three targeted other positions southwest of the town, he added. No casualties were immediately reported.
Residents contacted by AFP confirmed the raids but could not say if they were carried out by US drones or Yemeni forces.
Tuesday's violence follows a string of attacks by the jihadist network against security forces that have rocked Yemen since former president Saleh stepped down last month after a year-long uprising against his 33-year rule.
And it comes just hours after the interior ministry warned of "a terrorist plot by Al-Qaeda to target vital installations and government facilities in several provinces."
"The Al-Qaeda network is planning to carry out terrorist operations using bomb-laden vehicles," it said.
The ministry is committed to "dealing with this threat ... (and) will continue its war on terror."
Politicians in Sanaa accuse military factions still loyal to Saleh of colluding with with the extremist network, an allegation mostly strengthened after the March 4 attack.
They say factions led by Saleh's relatives are handing over arms to Al-Qaeda, which also frequently robs vans transporting Money to banks in an attempt to finance their operations.
On Monday, Al-Qaeda suspects attacked a van transporting money to the Cooperative & Agricultural Credit Bank in the main southern city Aden seizing $347,000, a police spokeswoman told AFP.
In an address to the nation after being sworn in on February 25, interim president Abdrabuh Mansur Hadi vowed to fight Al-Qaeda and restore security across the impoverished nation, ancestral homeland of slain jihadist leader Osama bin Laden.
Shortly after his speech, a suicide attack against a presidential palace in the mostly lawless southeastern province of Hadramawt killed 26 Republican Guards. Al-Qaeda in the Arabian Peninsula claimed responsibility.
The militants have also exploited the weakening central government in Sanaa to strengthen their presence especially across the country's south and southeast.
Critics charge that the new unity government headed by Prime Minister Mohammed Basindawa, a Saleh opponent, has been slow to react to Al-Qaeda's threats amid loud calls for Hadi to restructure the army, as per the Gulf-brokered plan that saw Saleh quit.
The March 4 attack came one day after Hadi named General Salem Ali Qatan to head the 31st Armoured Brigade in south Yemen, a post that General Mahdi Maqola, known for his close ties to Saleh and accused of corruption, had held for decades.
During his years in power, Saleh, a self declared US ally in its "war on terror," carefully chose his aides.
His son Ahmed still heads the elite Republican Guard units, while his nephew Yehya commands central security services and another nephew Tariq controls the presidential guard.
Saleh's half-brother, General Mohammed Saleh al-Ahmar, still commands air force units, despite nationwide protests calling for his ouster.
Residents in Sanaa say the former president continues to move across the capital enjoying the same security measures that have surrounded him while he was the head of state.