"My solidarity and support goes out to the families and friends of victims and all those affected by these tragic floods", Prime Minister Pedro Sanchez said on Twitter.
"Our most honest condolences to the loved ones of the victims of the serious floods in San Llorenc", he wrote.
Nadal's state-of-the-art academy opened in June 2016 and is in his home town of Manacor.More news: Storm Michael could soon form, hit USA midweek
Witnesses said a dry creek overflowed, creating a strong current of water and mud that buried cars and tore down trees.
A 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 also recovered from the garage of a house in Arta, another nearby town.
Two men were found dead around midday on Wednesday, one in the northeastern town of Arta and another at S'illot further south on the coast.
Hundreds of displaced residents are seeking shelter in emergency relief centres, while soldiers have been sent to assist the rescue effort, Spanish authorities said. "We had to swim to try to survive".More news: Why Camilla Parker Bowles Won't Be Attending Princess Eugenie's Wedding
In all, more than 500 people helped with rescue and cleaning up operations, as authorities said the rainstorm was unlike any people could remember. The flooding also affected phone communications and forced the closure of at least seven major roads.
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 weather agency, AEMET, said more heavy rainfall is expected Wednesday in eastern and southern parts of the Iberian peninsula.More news: Google+ gets the axe after exposing users’ private info