Sparks were seen as the aircraft slid along the runway, with the engine under the left wing scraping against the pavement.
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L.A. City firefighters responded to the airport around 3:50 a.m., according to Margaret Stewart of the Los Angeles Fire Department.
The crew of FedEx Flight 1026, a Boeing 767, could not extend the left main landing gear before touching down around 4:50 a.m. after a flight from Newark Liberty International Airport, said Ian Gregor, a spokesman for the Federal Aviation Administration.
One of the two pilots on board sustained a non-life-threatening leg injury while exiting the aircraft, according to Stewart. The other pilot was not injured.
FedEx said in a statement said that company officials "are working with investigators to fully understand the matter."
"We are grateful that our flight crew is safe and that no one was seriously injured," the company added.
The Federal Aviation Administration and National Transportation Safety Board will conduct an investigation, Stewart said.
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The runway, one of four at the airport, was closed pending removal of the aircraft, but airport officials did not expect delays due to the incident.
The Associated Press and City News Service contributed to this report.