The nursing home deaths brought the total number of storm-related fatalities in Florida to 20 and illustrated the urgency of restoring electricity to millions of people across the southern state.
Around 115 residents of the retirement home in Hollywood, north of Miami, were immediately evacuated after a nearby hospital began receiving patients suffering from heat-related problems.
"It's a sad event," Hollywood police chief Tomas Sanchez told a news conference. "We believe at this time they (the deaths) may be related to the loss of power in the storm."
"I am going to aggressively demand answers on how this tragic event took place," Scott said in a statement. "Although the details of these reported deaths are still under investigation, this situation is unfathomable."
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The governor said he has ordered a probe by state authorities.
"If they find that anyone wasn't acting in the best interests of their patients, we will hold them accountable to the fullest extent of the law," he said.
Sanchez, the police chief, said a criminal investigation had been launched.
Dr Randy Katz, medical director of the emergency department at Memorial Regional Hospital, said the hospital began receiving patients early on Wednesday.
"(We) quickly identified some issues inside the facility with fire rescue and immediately evacuated the building," Katz said.
He said most of the patients admitted to the hospital have been treated for respiratory distress, dehydration and heat-related issues.
Florida officials have made restoring electricity to the millions who have lost power a priority and tens of thousands of utility company workers, many from out of state, are engaged in the huge effort.
Irma, which made landfall Sunday morning in the Florida Keys as a Category Four hurricane, had triggered orders for more than six million people to flee to safety, one of the biggest evacuations in US history.
Some residents of the Keys were met with scenes of devastation on Tuesday after police lifted roadblocks and began allowing people to return to the string of islands off Florida's southern coast.
At least a quarter of the homes in the Keys were destroyed, according to federal emergency management officials, and 65 per cent suffered some damage.
"Bad, it's real bad," Keys resident Bryan Holley told NBC News.
"It's gonna take months, maybe years to get this cleaned up," said Holley, who ignored orders to evacuate and braved the storm on Cudjoe Key.
President Donald Trump and his wife, Melania, were to visit Florida to survey the damage on Thursday.