Airport spokeswoman Melissa Scovronski said Delta has canceled about 700 flights from the airport and other airlines have thinned out their schedules.
She said all four runways at the airport are now working, but airport officials expect they will be down to one runway by the end of the day.
Scovronski said travelers should check with their airline before going to the airport.
The National Weather Service has declared a winter storm warning for the Twin Cities with a prediction that 10 to 15 inches of snow could fall by midway Monday.
A blizzard warning for portions of west central and southwestern Minnesota has been declared through noon Monday.