Emergency services were called to the scene after the cyclist was hit at around 11.25m on Saturday, April 24.
The 50-year-old man was cycling along Spittal Terrace, near to Hamilton Road in Blantyre, when he was struck by a dark coloured Vauxhall Insignia.
The car did not stop at the scene.
Passers-by were able to call an ambulance and he was taken to the Queen Elizabeth University Hospital in Glasgow where he remains for treatment.
Medical staff describe his condition as serious but stable.
Sergeant Raymond Giulianotti, East Kilbride Police Station, said: "I have no doubt that the driver of the car would have known that they struck the cyclist who was seriously injured as a result.
"A number of witnesses have already come forward, however, we are particularly keen to hear from anyone who may have dash-cam footage from the area at the time.
"If you were either on Spittal Terrace or A724, Hamilton Road, heading from Blantyre to Cambuslang between 11.10 am and 11.30 am on Saturday morning, then please get in touch with officers.
"No matter how insignificant you think any information is please make police aware as it may assist in our enquiries."
Anyone with information about the incident can contact officers via 101 quoting reference number 1368 of Saturday, 24 April, 2021.
Alternatively, Crimestoppers can be called anonymously on 0800 555 111.