The airport was shut down on Monday but flights had been grounded since Saturday, in advance of the hurricane.
The terminal had remained opened for over 600 guests and another 40 stranded passengers who could not find lodging.
Report say operations at the MIA are expected to re-open with a limited schedule on Tuesday.
Nearby Fort Lauderdale-Hollywood International Airport, which also closed ahead of Irma, will also keep its doors shut Monday as it assesses damage and makes any necessary repairs.
The area surrounding the airport sustained extensive damage from 100 mph winds.
American Airlines began shutting down operations in Miami, Fort Lauderdale, Fort Myers, Sarasota and West Palm Beach by Friday afternoon and cancelled flights through the weekend.
JetBlue Airways said on Wednesday afternoon that it had cancelled about 130 flights.
American, JetBlue, United and Delta offered waivers letting customers change travel plans to Florida and the Caribbean without the usual charges for changing a ticket. Dates and covered locations varied.
Hurricane Irma’s attack comes few weeks after hurricane Harvey devastated Houston, Texas.