Around 3:30 pm, a silver coloured Ford Fiesta was travelling northbound on the M73 northbound off-slip road to the M8 (J8) when the vehicle appears to have lost control and crashed into a ditch on the grass verge.
Emergency services attended and a 95 year old woman was pronounced dead at the scene.
The 68-year-old female driver was taken to the Queen Elizabeth University Hospital in a critical condition.
The road was closed as crash scene investigators conducted enquiries at the scene.
An investigation to establish the circumstances is underway and officers are appealing for anyone who may have seen the incident to contact them.
Motorists are also being asked to check any dash cam footage which may have captured detail which could be relevant to the investigation.
Anyone with information should call Road Policing Officers at Govan OSD Complex via 101.