Two British nationals are among those among the confirmed dead.
A statement from the Foreign Office said: "We are in contact with the Spanish authorities responding to flooding in Majorca, and urgently seeking updates from them".
The Balearic Islands' emergency services spokeswoman, who wasn't authorized to be named in media reports, told The Associated Press that the body of a Dutch woman was recovered from the garage of a house in Arta, another nearby town.
The town of Sant Llorenc is around 60 kilometres east of Palma - the capital of the Mediterranean island.
Footage broadcast of the floods showed cars being swept away by the rampaging flood waters and many people remain trapped in their homes following the heavy rain which hit the region.
The British couple believed to have been killed were said to be travelling in a taxi when the vehicle was caught in the flood.
"In just two hours, some 180 litres of rain fell and we realized that we could not control the water", she said.
According to the Spanish weather agency, more heavy rainfall is expected in eastern and southern parts of the Iberian peninsula.
Most of the victims were discovered in the town of Sant Llorenc and another in S'illot.
The regional government called an emergency meeting, and authorities said rescue workers and military units had been sent to the area to help.
Lawmakers held a minute's silence before the weekly prime minister's question time on Wednesday morning.