A spokeswoman with the regional emergency service said two British nationals and a Dutch woman were among the victims, but she couldn't confirm whether six more people were still missing at midday as local media reported.
The deputy mayor of the town, Antonia Bauza, confirmed to Cadena SER radio that two of the victims were British, while two others killed in the town were locals.
Spain's meteorological office warned that rainfall and storms were set to get worse in the archipelago "in the coming hours".
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.
Two of those killed were in Sant Llorenc, one in Arta and two more in S'Illot.
Image Heavy rain and flash floods hit Sant Llorenc de Cardassar on the island of Mallorca Spain
"My honest condolences to the relatives of the deceased and injured by the severe floods in San Llorenc".
Swamped streets and piles of overturned cars, some of them along the guardrails of a major road, were a common sight in Sant Llorenc and other nearby towns on Wednesday.
Hundreds of people spent the night in emergency shelters and schools remain closed on Wednesday.
The Spanish parliament held a tribute to the victims in the form of a minute's silence. The flooding also affected phone communications, destroyed two bridges and forced the closure of 11 roads.
Some parts of the island received up to 23 centimetres of rainfall in around four hours on Tuesday evening, national weather authorities reported.
"What is most urgent right now is to find missing people and address the concerns of their relatives and all neighbours", Prime Minister Pedro Sanchez said during a visit to the disaster zone.More news: Saudi leadership ordered Khashoggi's murder, Turkey says