Police received “multiple 999 calls” after the VW Golf pulled on to the dual carriageway at about 9pm on Thursday.
Devon and Cornwall Police say at least two vehicles, including an HGV, reported near misses as the car travelled towards Plymouth.
A 53-year-old woman was arrested on suspicion of dangerous driving, driving while unfit and failing to provide a breath test.
A force spokeswoman said: “Police received multiple 999 calls from the public just after 9pm on Thursday, November 14, after a car was seen travelling on the wrong side of the A38 in the Ivybridge area.
“The VW Golf was being driven southbound towards Plymouth on the northbound carriageway.
“At least two near misses were reported, including one from an HGV driver.
“Other motorists signalled the driver about the danger.
“Police attended and the vehicle stopped just past the Saltram overbridge in the outside lane a short time later.
“The on-slip northbound was closed at Marsh Mills while the vehicle was moved off the road.
“A 53-year-old woman, from Kingsteignton, South Devon, was arrested on suspicion of dangerous driving, driving while unfit through drink or drugs and failing to provide a breath test.
“She has been released under investigation.”