The fight followed attacks by gunmen at a commercial bank, military base and police station in the town of Gashua in Yobe State, All Africa reported Friday.
In the bank attack, gunmen took more than $56,000 in U.S. currency after they forced the manager to open the vault, said Sanusi Rufai, the state police commissioner.
Police said they seized guns, hand grenades and ammunition from the attackers and one of them was captured.
Gashua had been placed under siege by security forces earlier in the day after the attacks on the military base and police station, China's state-run Xinhua news agency reported.
Similar attacks in neighboring Borno State last week killed at least 185 people.