Officers say the incident took place at the junction of Broomfield Street and Gartlea Avenue at around 9pm on Tuesday, January 2.
The vehicle, which is described as being a dark-coloured saloon car, is understood to have hit a man and then drove off.
Following that, a 23-year-old man was found injured and taken to hospital.
Now, cops are appealing for information following the incident.
Sergeant Stewart Taylor, of the Road Policing Unit in Lanarkshire, said: “Our enquiries into this incident are ongoing and I would urge anyone with information which could help to get in touch.
“We would also be keen to speak to anyone who have dashcam or private CCTV footage from the area.
“Anyone who feels they may be able to help is asked to call 101, quoting reference 3050 of January, 2, 2024.”
