Shayef Mohammed Said al-Shabwani was "one of Al-Qaeda's most dangerous and wanted commanders... Suspected of involvement in abductions and killings of Yemeni police and foreigners," the spokesman told state news agency Saba.
He was stopped in a car close to the presidential palace with four other people, one of whom was also killed in an exchange of fire when they resisted arrest, the spokesman said.
The other three were arrested, two of them wounded, he added.
Yesterday, troops entered the town of Azzan, the second largest in Shabwa province, from which Shabwani takes his name.
The jihadists had controlled much of Shabwa and hill districts of neighbouring Abyan and Baida provinces since 2011.
There has been a wave of kidnap attempts against Western embassy personnel in the capital in recent weeks, some of them deadly.
