A police spokesman said the suicide bomber and a traffic police officer were killed and many other police officers were injured trying to flee, The (Lagos) Nation reported.
The National Emergency Management Agency said emergency workers in the capital were using body bags, ambulances, a hydraulic spreader and cutters to respond to the explosion, CNN reported.
"It's serious, very serious, as so many cars are on fire," Umar Mariga, a spokesman for the National Red Cross, told CNN.
Police officials said the bomber drove his explosives-laden car into a parking lot and then detonated, The Nation said.
Police said the Islamic fundamentalist group Boko Haram was behind the attack. Boko Haram has been operating in Maiduguri and other states in northeast Nigeria.
The blast shattered windows as high as the seventh floor of the police headquarters, police said. More than 70 vehicles were either damaged or destroyed.