Two were taken to nearby shock centers and three others were taken to local hospitals with life-threatening injuries, the Miami-Tate Fire Rescue said. Injuries to a sixth person were not immediately available.
The Federal Aviation Administration said in a statement that the single-engine Cessna, which was flying from Fort Lauderdale-Hollywood International Airport, lost power while landing and collided with a vehicle on the bridge.
The FAA said there were three people on board.
Video taken from the balcony of a nearby hotel by Alex Hooperman, who lives in Miami, shows a small, wrecked plane on fire, with black smoke rising from it.
Several feet away from the plane was a maroon SUV that appeared to have caused extensive damage, the video shows, which may have been the vehicle that collided when the plane tried to land.
Hooberman said he saw at least two people getting off the plane, and many more were placed on stretchers by emergency personnel.
Chad Rane, who filmed another video of the crash, told CNN that there was a boat in the marina next to the bridge and that he heard an explosion.
He went upstairs to see what had happened and recorded the aftermath of the accident. His shots showed dark smoke rising over the plane.