The attack occurred just before King Juan Carlos was due to arrive on the island Saturday, the Zarzuela royal palace told DPA.
The only members of the royal family who could have been on Majorca Thursday were princesses Elena and Cristina, but that could not be confirmed, the sources said.
The explosion followed a car bombing staged by suspected ETA militants, who targeted a police barracks in the northern city of Burgos Wednesday. The attack caused injuries to about 60 people.
The attack on Majorca occurred one day before ETA marks its 50th anniversary Friday. It also coincided with the 18th anniversary of two other attacks which injured several people on Majorca in 1991.
ETA, which is listed as a terrorist organisation by the European Union and the United States, has killed about 850 people in its campaign for a sovereign Basque state.