Police had not released the identities of the dead or their relationship late Friday, the Minneapolis Star-Tribune reported.
Police said they got a report at about 7:30 a.m. of a red Saab that was being driven erratically on Highway 212 in Chaska, Minn. Soon after, the Saab struck another vehicle in the rear and sped up the highway.
Officers from the State Patrol, Carver County and Chaska pursued the car at speeds that sometimes reached 90 mph, police said. In Eden Prairie, about 10 miles northeast of Chaska, police used stop sticks that punctured two of the Saab's tires and it crashed into a noise barrier.
The Bureau of Criminal Apprehension is investigating the shooting. Police have said only that shots were fired after a man and woman got out of the Saab and there was a struggle.
A section of Highway 212 was closed through the day, tying up traffic during the morning and evening rush hours.