Emergency services were called to the collision on the A725 East Kilbride expressway at around 6.45am on Saturday.
The man riding the motorbike was pronounced dead at the scene, Police Scotland confirmed.
The man driving the car was arrested and subsequently taken for treatment to Hairmyres Hospital in the South Lanarkshire town, officers said.
A force spokeswoman said: “The car appears to have been travelling in the wrong direction when the collision occurred.”
The road was expected to be closed for a number of hours following the incident, with motorists advised to use alternative travel routes.
Anyone who witnessed the incident is being asked to contact the divisional road policing unit on 101, quoting incident number 0927 from Saturday.