Airport spokesman Marc Henderson told The Miami Herald on Thursday night that one plane had a damaged wingtip and the other sustained damage on the tail section.
The collision happened between Concourses J and H as an incoming Aerolineas Argentinas Airbus with 240 passengers aboard struck an Air France 777-300 plane preparing to leave for Paris with 350 passengers on board.
Henderson says rescue crews quickly surrounded both planes.
The Herald reports the passengers arriving from Argentina were allowed to get off the plane at the gate. The passengers heading to France had to pick up their luggage and wait in long lines to reschedule their flights.
An investigation is under way.