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.
Security forces have been on high alert in the capital since the army launched a highly publicised offensive against Al-Qaeda in its southern strongholds late last month, drawing open threats of retaliation.
On Thursday, 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.