The bitter weather comes after a heavy snowstorm hit much of the region last week. Schools in Chicago and other Midwest cities were closed and people warned to stay indoors.
More than 1,000 flights were cancelled on Sunday at airports throughout the Midwest.
“It’s just a dangerous cold,” said a National Weather Service spokesman.
The forecast is extreme: -35C in North Dakota, and -26C in Minneapolis, Indianapolis and Chicago. Wind chills – what it feels like when high winds are factored into the temperature – could drop into the -45 to -50C.
In New York the temperature was expected to drop sharply from about 11C to about -12C overnight as arctic air moved in.
Many parts of the US have not been so cold for almost two decades. Officials warned that frostbite and hypothermia can hit within minutes.