The blast occurred at the Living Faith church near the capital of Nigeria`s northern state of Bauchi, they said.
No group has claimed responsibility but the attack bears the signature of a radical Islamic militant sect - Boko Haram.
The Boko Haram Islamist sect claimed responsibility for three church bombings.
Egyptian officials said there were hints of "foreign elements" being behind blast.
Local police say damage to the church caused by blast was not significant.
Day in Pics: 29th December
Showbiz World - December 29, 2014
Stars celebrate Christmas