The attacks rocked the town of Ashaka in Gombe state late Wednesday and saw gunmen also use explosives, said police spokesman Ahmed Mohammed.
“There were coordinated bomb and gun attacks on a divisional police station and two banks in Ashaka town last night,” Mohammed told AFP.
“The police station was completely burnt down by the attackers using explosives. The two banks were also badly damaged.
“We have lost four men in the attacks, including the divisional police officer,” he said, referring to the local police chief.
He said an investigation had been opened and it was not yet clear who was behind the violence, though scores of such attacks have been attributed to Boko Haram, which has killed hundreds in shootings and bombings.
It was not known why Ashaka was targeted, though the town is an important economic centre for the area and houses Ashaka Cement, a subsidiary of French firm Lafarge.
The two banks attacked were said to be located within the cement company premises for business-related transactions.
Boko Haram has been blamed for increasingly deadly and sophisticated attacks in Nigeria, Africa’s most populous nation and largest oil producer.
Police have often been targeted, while authorities say the group has robbed banks to help finance their operations.
Violence blamed on the sect, whose goals remain largely unclear, has since 2009 claimed more than 1,000 lives, including more than 300 this year, according to figures tallied by AFP and rights groups.