The woman was stopped by police on the E18 motorway near Västerås, Swedish Radio reported, after the car was seen swerving across the road.
The girls told police that they had kept the car on the road after the woman fell asleep as the car was travelling at 140 km per hour.
The woman had a blood alcohol level of 1.4, and police suspect her of driving under the influence of alcohol, dangerous driving and other serious traffic offences.
Police in Västerås told Svenska Dagbladet that the woman was “very drunk, and has not been able to be questioned yet.”
The girls were being taken care of by social services.