Footage from Sant Llorenç des Cardassar town in the east of the island, one of the worst-hit areas, showed streets inundated with fast-flowing, muddy water. Emergency services in the town said at least two people were swept away by floodwater when rivers burst their banks.
Two more people were killed in the town, along with two further victims, who died in the coastal town of S'illot, the BBC reported.
Spanish Prime Minister Pedro Sanchez was scheduled to visit the affected areas later in the day and the police said rescue efforts to locate nine others declared missing in the adverse weather conditions were ongoing.
"I'm closely following the devastating news coming from Sant Llorenç (Mallorca)," Sanchez said in a tweet. "My solidarity and support to the families and friends of the deceased and to all those affected by these tragic floods."
The Spanish military deployed more than a hundred emergency workers with sniffer dogs. Three helicopters and a Hercules military transport plane were sent from the mainland Spanish city of Valencia to help with search and rescue efforts, reports say.
The Spanish Parliament held a minute's silence in a tribute to the victims.
Around 100 people spent the night in a sports centre in the nearby city of Manacor, which was on standby to provide shelter to those unable to reach their homes or had been forced to abandon them.
Up to 220 litres of water per square metre fell on Tuesday evening in Sant Llorenç, the government said.
Mallorca is one of the country's main tourist destinations.
(With inputs from agencies.)