Emergency services said the 0630 (0430GMT) blast at the Plaza Callao business and shopping district in the centre of the Spanish capital had caused extensive damage.
Four of the injured were taken to hospital and the rest were treated at the scene.
Police believe the car had been carrying about 15 kg (33 lbs) of explosive, and bore the hallmarks of the Basque separatist group ETA.
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ETA's bloody record | |
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Leaders in the shadows | |
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Timeline: Key events | |
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The Irish connection | |
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Who are the Basques? | |
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The blast shattered windows in all 10 storeys of the store and in some buildings across the nearby Gran Via boulevard.
The blast came four days after a bomb exploded outside a newspaper office in Spain's Basque region in an attack blamed on ETA.
Police also defused a bomb attached to the underside of a van in a small Basque town.
ETA has been linked to five killings since calling off a 14-month ceasefire last December. The group has been blamed for about 800 deaths since taking up arms in 1968.