Southwest Flight 1905 had just landed following a flight from Oakland, Calif., when the mishap occurred just before 5 p.m., KMGH-TV, Denver, reported.
The 125 passengers and five crew members aboard the Boeing 737 were reported to be unscathed, the TV station said..
Passenger Brad Harris said the Boeing 737 was turning onto a taxiway when it "hit a patch of ice." Two of the three landing gears went off the pavement, he said.
"The pilot hit the engine I guess to stop the plane or slow the plane down, so there is engine noise as the plane is trying to stop," Harris said. "And then the front wheels and then the rear wheels then just slid off the runway and into the grass."
Denver firefighters helped escort the passengers off the aircraft and onto a bus to be shuttled to the terminal.
KMGH-TV said there was about an inch of snow on the ground when the incident occurred.
Airport operations remained normal after the accident, airport spokeswoman Jenny Schiavone said.