Emergency services rushed to the scene on James Street at its junction with Kirkton Street at around 3:07 p.m. following reports of a serious accident.
A woman in her twenties was also injured.
The four victims are being treated at Queen Elizabeth University Hospital in Glasgow, but the extent of their injuries is currently not known.
There is a huge response of mercy at the scene, including 10 ambulances and specialist trauma teams.
A spokesperson for the Scottish Ambulance Service said: “We got a call at 3:07 pm to witness an incident on Kirkton Street, Carluke and sent 10 resources to the scene.
“A woman in her 20s and three children were transported to Queen Elizabeth University Hospital in Glasgow. ”
A major investigation has been opened and the cops are asking anyone who witnessed the crash to make contact.
Scottish Police Inspector William Broatch of the Motherwell Road Police Unit said: “At approximately 3:10 pm the police were called to James Street in Carluke, at the junction with Kirkton Street, following a ‘a report of a road accident involving a car and four pedestrians – a woman and three children.
“Pedestrians are all taken to hospital for treatment. Emergency services remain on site and local diversions are in place.
“Anyone with information about the incident can call the police on 101, citing incident 2110 of October 27. “