The 13-year-old was hit by a small, silver vehicle in Main Street in Bothwell, near to the Clydesdale Bank at 2.50pm on Monday.
He was taken to Wishaw General Hospital for treatment following the collision.
Inspector George McCutcheon, of Hamilton Police Station, said: "We are looking for the public’s help to trace the driver of the vehicle, who failed to stop after the collision.
"I would ask anyone with any dashcam and mobile phone footage of the incident, or anyone who was in the area around the time of the collision, to please get in touch with officers.
“I would also make a direct appeal to the driver of the car involved to do the right thing and come forward."
Anyone with information can contact police on 101 quoting reference number 1769 of Monday, 5 April, 2021.