Prime Air Flight 7598 from San Juan, Puerto Rico overran the airport's diagonal runway at about 2pm on Sunday (4am Monday AEST) and was disabled at the airport's northwest end, officials said.
Five people were killed, three critically injured and two others hospitalised with less severe injuries, Miami-Dade County officials told a news conference.
Miami officials said it was too soon to determine whether the people who died were on board the plane or in the vehicles the plane hit.
The crash, which sent thick black smoke billowing into the sky, trapped the pilot and co-pilot in the cockpit and some occupants in cars, said Miami-Dade Rescue Fire Chief Ray Jadallah.
The agency said another person was trapped under a vehicle.
It also halted flights at the busy travel hub for much of the afternoon. Fire crews were still dealing with a fuel leak on the plane several hours after the crash, Jadallah said.
All runways and taxiways at the Miami airport were closed as of 3pm EDT. Travelers should "expect significant delays and potential cancellations", US Transportation Secretary Sean Duffy said in a post on x.
The plane came to rest beside a roadway near two semi-trucks, images from the scene showed.
The aircraft appeared to be resting on its belly and was largely intact despite the fire.
The flight had been operated by 21 Air, a cargo carrier based in North Carolina.
The 32-year-old Boeing 767 was originally built to carry passengers and flew for several airlines for more than two decades before being converted to a cargo plane in 2015, according to flight-tracking site Flightradar24.
About 250 flights were delayed at the airport late on Sunday, according to FlightAware, a website that tracks flight disruptions.
The National Transportation Safety Board said it is sending a team to Miami led by Chairwoman Jennifer Homendy to investigate.
Amazon said in a statement that it would co-operate with any investigation.
"We're heartbroken to learn that five people lost their lives in today's incident at Miami International Airport," the company said.
"Our deepest sympathies go out to the families, loved ones, and all those affected by this devastating loss."
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