The offensive on Saturday followed intelligence that the extremist group planned to attack the restive city of Damaturu again, said the deputy police spokesman of Yobe state.
“Security operatives were able to discover a plan by Boko Haram hoodlums to launch attacks in the city,” said Gbadegesin Toyin.
The Joint Task Force (JTF) military unit “located their positions… they cordoned off these positions and engaged the gunmen in a shootout,” he added.
He said soldiers fired mortar rounds at the Islamist militants, who responded with gunfire and also threw improvised explosive devices.
The violence was most heavily concentrated in the Nyanya and Obasanjo Estates areas of the city, he said.
“Three suspected Boko Haram militants were killed and a female sect member was arrested. The hideout was destroyed in the raid,” Toyin added.
Nigerian authorities on June 19 slapped a round-the-clock curfew on Damaturu, after suspected Boko Haram Islamists launched coordinated gun attacks on targets around the city.
The curfew was partially relaxed two days later after soldiers and police reclaimed control of the streets in an offensive that left at least 40 people dead, including 34 alleged Boko Haram members.
The ban on movements was further eased on Monday, but Damaturu residents are still forced to remain in their homes between 6:00 pm and 7:00 am.
The government’s response to Boko Haram in past months has included heavy-handed military raids, which had angered residents of hard-hit areas and failed to stop the extremists.
Last week, President Goodluck Jonathan fired his national security adviser and defence minister, amid intensifying criticism of his administration’s response to the Boko Haram threat.