The State Security Service said Emin Jami tried to set off an explosive belt while resisting arrest today, but was shot dead in the capital, Baku, before he could.
The service says Jami had a previous conviction for being part of an extremist group.
It says he had been linked to "international terrorist organizations and illegal armed groups involved in military conflicts abroad," but didn't offer any specifics.
The government in Azerbaijan, a Shia Muslim ex-Soviet nation, has methodically cracked down on suspected radical Islamists.