No injuries were reported among the plane's 180 passengers, the Detroit News reported.
Flight 2283 "slid off a taxiway onto a grass area about approximately 6:40 a.m.," Delta spokesman Morgan Durrant said in a statement. "Delta technicians are working to move and inspect the aircraft."
Passengers were to leave on another flight later Monday morning.
Police and fire personnel were dispatched to the scene.
There was no indication the accident was weather-related.