The attack Sunday was one of at least four explosions across Africa's most populous nation on Christmas Day.
A radical Muslim sect known as Boko Haram has claimed responsibility for attacks on two churches that left at least 25 people dead.
Local police commissioner Tanko Lawan said the suicide car bombing happened around noon in the Yobe state capital of Damaturu, targeting the headquarters of Nigeria's secret police in the area.
In the last year, Boko Haram has carried out increasingly bloody attacks in its campaign to implement strict Shariah law across Nigeria.
