In a statement, a United spokesperson said the seat belt sign was illuminated when the Boeing 757 hit the turbulence.
The airline is "conducting a review."
There were 129 passengers and 8 crew members on board. The plane was met by medical personnel on the tarmac, and the passenger who was sent to the hospital was released within a few hours, United said.
It's unclear if the injured passengers were wearing their seat belts at the time, but it's always a good idea to be strapped in - even when the sign is off.