Broward County Mayor Barbara Sharief said three were found dead at the nursing home in the city of Hollywood. Three others died in hospital.
Ten million people are still without power in Florida, Georgia and the Carolinas after Hurricane Irma.
The storm - which has claimed more than two dozen lives in the US - struck southwestern Florida on Sunday morning as a category four hurricane before weakening to a tropical depression on Monday.
Irma earlier left a trail of destruction in the Caribbean, where nearly 40 people were killed.
Hollywood Police Chief Tomas Sanchez said the Rehabilitation Center at Hollywood Hills facility has been sealed off and police are conducting a criminal investigation.
State investigators from the Florida Office of Attorney General were also at the scene, city officials said in a statement.
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