The injury happened Wednesday afternoon on a United Airlines flight headed to O'Hare International Airport while the airplane was over Louisiana, officials said.
The flight was diverted to Memphis, Tennessee. Paramedics met the aircraft at the gate at Memphis International Airport and took the passenger to the hospital.
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Chicago-based United said the 737-900ER aircraft had 172 passengers and seven crew members on board. The airplane was scheduled to resume its flight to Chicago on Wednesday afternoon.
The Memphis Fire Department said six other people declined treatment and transport to the hospital, but the extent of their injuries was not known.
The FAA is investigating the incident.
No further information was immediately available.
AP News contributed to this report.