Motorcycle-mounted gunmen later shot at a third police station in another part of the city, said Sokoto state police spokesman Sani Dahiru. He could not immediately say how many gunmen there were, or whether there had been casualties.
The twin explosions and drive-by shooting come as Nigeria faces an increasing threat from a radical Islamist sect known as Boko Haram.
There has also been a spate of recent attacks targeting uniformed officers, some of which have been blamed on the sect.
Three gunmen killed a shoe-shiner Monday morning outside an uninhabited house belonging to Nigerian Vice President Namadi Sambo in the north central city of Zaria, said Kaduna state police spokesman Abubakar Balteh. He said the house had been under renovation and that the man was near policemen who had been guarding the construction site.
Rioters had burned down that same house during postelection violence that swept across northern Nigeria after April 2011 presidential polls, Balteh said.