At least another six people were still missing, El Pais newspaper and other media reported, though emergency services on the island - which is popular with foreign tourists - could not confirm that figure.
"My honest condolences to the relatives of the deceased and injured by the severe floods in San Llorenç".
Videos shot on mobile phones by local residents showed a strong current of water and mud that buried cars and tore trees on its way down the streets of the town of 8,000.
"It all happened in less than 10 minutes", an unidentified witness with wet clothes told the public broadcaster TVE. Angela Alfaro had to spend the night in a shelter because a road section leading to Sant Llorenc had collapsed.
Officials have said more than 600 rescuers and medical staff were at work and that emergency relief centres had been set up in sports halls.
"We have lots of vacation homes", Bauza said. In all, more than 500 people helped with rescue and cleaning up operations, authorities said.
Hundreds of displaced people are now being forced to shelter in emergency accommodation.
Footage broadcast on Spanish television showed raging, muddy waters rushing down roads, houses flooded and vehicles piled on top of each other after the Mediterranean island was pounded with heavy rain in just a few hours.
The thunderstorms are still circulating in the region and further torrential rain is expected on Wednesday and Thursday, with southern France and northwest Italy being most at risk of flooding.