The accident happened at The Centre roundabout in Cornwall Way, East Kilbride, at around 1.30pm today.
The 91-year-old man who was driving the car and his 86-year-old wife were freed from the vehicle by paramedics and taken to Hairmyres Hospital in the town.
The woman died a short time later and her husband remains in a serious condition in hospital, police said.
No other vehicles were involved in the crash and officers are appealing for any witnesses.
Constable Ann Alexander said: "The roundabout is near the bus stop and is a busy area for traffic. I would ask that anyone who saw the crash or who have any information that will help with our enquiries, contact officers at Motherwell."
Police can be contacted on 101.