Islamist sect Boko Haram wants to carve an Islamic state out of Nigeria. It and other Islamist groups have become the main threat to stability on Africa's top oil-producing state and increasingly menace neighbors like Cameroon.
Boko Haram has killed hundreds in gun and bomb attacks, including 25 in Kano earlier in March, since it intensified an insurgency two years ago.
In Sunday's raid, one soldier was killed and another seriously injured while a suspected suicide bomber was arrested in a car packed with explosives, the army said.
"This operation was conducted following a tip-off from our intelligence. You can see that there are over 10 of the terrorists all dead," Iliyasu Abbah, an officer in the military task force dealing with Islamist rebels, told Reuters.
Task force spokesman Ikedichi Iweha confirmed 14 suspected terrorists had been killed. A witness, who asked not to be named, said he saw a woman and a child among the dead.
Security was stepped up in northern Nigerian cities this weekend to cope with an increased threat posed by Islamist groups during Christian holidays, when churches have been targeted by suicide bombers.
Western governments fear that ties with groups like al Qaeda's North African wing are drawing Nigerian Islamists towards a more explicitly anti-Western agenda.