Kaduna, in the mainly Muslim north, has been the target of several attacks by Boko Haram since the group's low-level insurgency intensified over two years ago.
"The exchange of fire that ensued resulted in the death of five terrorists, while two that sustained various degrees of injuries are being treated."
Usman said seven rifles, detonating cord, remote detonating switches and IED materials were found and destroyed.
Boko Haram has killed hundreds this year in a campaign to impose Islamic sharia law in northern Nigeria. The sect is the biggest threat to stability in Africa's biggest oil exporter.
In its stronghold in the far northeast city of Maiduguri, seven people were murdered by unidentified attackers on Wednesday, a police spokesman said. A witness said he saw the seven dead bodies, all with their throats cut.
Gunmen killed six people at a church in the northeast town of Potiskum on Tuesday, the third year running that Christmas services have come under deadly attack.
But Boko Haram is not the only threat in northern Nigeria.
Islamist group Ansaru, known to have ties with Boko Haram, has risen in prominence in recent weeks. It claimed an attack on a major police barracks in the capital Abuja last month, where it said hundreds of prisoners were released.
The group said on Saturday that it was behind the kidnapping of a French national last week and it has been labeled a "terrorist group" by Britain.
Security has been tightened throughout the north of Africa's most populous nation and Christmas attacks weren't on the scale of the previous two years when dozens were killed in bomb and gun strikes.
At least 2,800 people have died in fighting since Boko Haram launched an uprising against the government in 2009, watchdog Human Rights Watch says.
The group, which is loosely modeled on the Afghan Taliban, mostly focuses its attacks on the security forces, religious targets and politicians.