The Broward County Sheriff's Office said an engine caught fire on the Boeing 767, which was getting ready to depart for Venezuela.
Mike Jachles, the spokesman for the sheriff's office, told WSVN 7 News television that "three people will be sent to area hospitals. There may be as many as seven injured in all."
"There is no fire now," he said, adding that the plane was quickly evacuated.
Video images circulating on the Internet showed a large cloud of black smoke pouring from the plane. Other images showed a fire-damaged engine under one of its wings.
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The plane was operated by Dynamic International Airways, a US-certificated airline that only recently had begun flights between Fort Lauderdale and Caracas' Simon Bolivar International Airport.
"Still waiting to hear the extent of injuries. And exactly what happened. But looks like quick action really made a big difference here," Representative Debbie Wasserman, whose congressional district includes Fort Lauderdale, said on CNN.
Waserman noted that there is a large Venezuelan community in Broward County.
The Federal Aviation Administration said flights in and out of the Fort Lauderdale airport were suspended following the incident.