The bomb may have been aimed at a military parade
Security forces were unable to find the bomb after searching the city's main Colon Square, and permitted planned national holiday celebrations - including a military parade attended by King Juan Carlos and Spanish Government members - to go ahead.
The bomb later went off in a car in an underground car park, blasting a large hole in its floor. Most of the injured were treated on the spot for smoke inhalation.
Parking officials had towed the car to the car park after finding it illegally parked on a pedestrian crossing.
Authorities said four of the injured were police officers.
Madrid mayor Jose Maria Alvarez said 66 cars and 15 towing vehicles were damaged, but no people were trapped inside.
A fire department spokesman said the blast resembled the car bomb explosion at Madrid's Barajas airport in August.
Continuing campaign
Police inspected the area but found no suspicious vehicle.
The BBC's Flora Botsford in Madrid says ETA has been relatively inactive since the terrorist attacks in the US, leading the Spanish Government to hope the new international atmosphere of co-operation against terrorism would finish ETA's violence once and for all.
This may be a sign the group means to continue its 30-year campaign for an independent Basque homeland, our correspondent says.
Theatre-goers
Our correspondent says that the normally crowded streets of Madrid on Friday night were fairly quiet as it was raining when the bomb exploded.
Theatre-goers watching a play near the site of the explosion said they were shaken by the blast during performance.
"We heard the explosion and the building shook but we thought it was part of the show because the actors kept acting," one man told Reuters news agency.