The island was hit by devastating floods overnight, with torrential rainstorms hitting the town of Sant Lorrenc, about 40 miles east of the capital Palma.
"The situation is a disaster and we're trying to locate survivors and help people but everything is flooded and people can not leave their homes", said Antonia Bauza, a senior official at San Llorenc mayor's office.
Videos posted online showed cars floating down the street in floodwater that was several feet deep.
Spanish authorities say that a total of five people have died, and a further 12 are missing.
Hundreds of displaced people are now being forced to shelter in emergency accommodation.
Incident involving Twins’ Sano under investigation in Dominican Republic
Gillandeux suffered breaks to both the tibia and fibula of his left leg and was taken to the hospital by Sano, according to Duran. According to the police report, Sano had "no documents on him and the truck had no plates" and "ran over a cop's foot and leg".
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.
100 rescue workers have been deployed to the area, and will be joined by 80 soldiers.
The British Foreign Office said it is "urgently seeking updates" from local authorities after reports that two Britons were among those killed.
Sanchez will be flying to the area later Wednesday, his office said.
Lawmakers held a minute's silence before the weekly prime minister's question time on Wednesday morning.
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