It happened at around 5:30 p.m. local time Tuesday at Nashville International Airport.
Officials say a tire blew out or collapsed.
133 passengers and 5 crew members safely evacuated the plane.
Authorities say most of the victims have minor injuries, one had chest pain.
The FAA released a statement Tuesday night:
Southwest Airlines 31, a Boeing 737 aircraft, rolled off a taxiway into the grass and got stuck while taxiing to its gate at Nashville International Airport at 5:30 pm Central Time. Passengers left the aircraft via stairs and were bussed to the terminal. The flight just landed from Houston Hobby Airport. The FAA is investigating.