If confirmed as ETA attacks, the blasts would conflict with government assertions that the group is seriously weakened after major police crackdowns in Spain and France in recent years.
The 50th anniversary of ETA's founding is Friday and the group may be trying to demonstrate with attacks on the two consecutive days before the milestone that it was not in any danger of breaking up.
Thursday's victims belonged to the paramilitary Civil Guard, which is chiefly in charge of policing rural areas and guarding official buildings. Mallorca is one of Spain's top tourist destinations and the explosion occurred at the height of the summer holiday season.
Television images showed the charred and mangled remains of a vehicle that had been parked on a street in the Palmanova beach resort area, southwest of the island's capital, Palma de Mallorca.
The cause of the explosion was under investigation. News reports said the explosion may have been caused by a bomb attached to the underside of a police patrol vehicle.
"State security forces have sealed off the island to avoid the escape of the terrorists," a regional Interior Ministry statement said.
"This means that all exit routes via the port, the airport and the sports marinas of Mallorca are closed." Incoming flights and ferries were not affected.
The blast occurred shortly before 2 p.m. (1200 GMT, 8 a.m. EDT). The Interior Ministry said several people were injured but none was in serious condition.
ETA is now blamed for nine attacks this year. The group has killed more than 825 people since it launched a violent campaign in 1968 for an independent homeland in Basque region of northern Spain. The group was founded July 31, 1959.
ETA did not phone in a warning before the Burgos attack as it typically does before most attacks, so authorities had no time to evacuate the 14-story building.
There were around 120 people in the barracks and surrounding buildings, a third of them children, at the time of the early morning blast.
The interior minister said the van had false license plates and had probably been stolen in France.
Spain has vowed to crush the separatist group since ETA ended what it had said was a permanent cease-fire with a bombing that destroyed a Madrid airport parking garage and killed two people in 2006.
