Three small bombs exploded on Sunday in places frequented by tourists in the capital of the island of Mallorca.
The first bomb exploded at a restaurant after it was evacuated. The second was found by police in another restaurant nearby and the third exploded in a shopping area beneath the central square in Palma.
The website of the Spanish newspaper El Mundo reports a phone warning was earlier made in the name of the Basque separatist group ETA.
The ambulance service was quoted as saying there had been no reports of injuries.
The attacks are not the first on Spanish holiday resorts: a car bomb on Mallorca on 30 July killed two officers of Spain's civil guard.
Bombings were also carried out in Spain, in the northern city of Bilbao on 19 June and the city of Burgos on 30 July.
ETA is blamed for the deaths of 828 people in its campaign for an independent Basque homeland in northern Spain and southwest France. It is considered a terrorist organisation by the European Union and United States.