The twin-engine Bombardier CRJ700, operated as a United Express commuter flight from Aspen to Denver, made a normal landing at about 2:20 p.m. local time and was on the taxiway before the flight crew was alerted to the fire electronically, SkyWest spokeswoman Marissa Snow said.
She said there was no indication of an engine problem until the plane was on the ground.
No injuries were reported among the 59 passengers and four crew members aboard the plane, she said.
Denver Fire Department personnel extinguished the flames, airport spokesman Heath Montgomery said, adding there "were no substantial impacts to airport operations."
"The fire was contained to one rear engine and flames were extinguished in a small amount of time," fire department Captain Robert Miller told Reuters.
Montgomery said the National Transportation Safety Board was notified of the incident. Snow said the cause was under investigation.