The boy suffered a cut to his chin and bruising to a leg.
"The child required a few stitches, that's why we are now investigating the incident," says Helsinki police sergeant Petri Jehkonen.
The driver was a young woman described as being fair and wearing a pink sweater, operating a burgundy-red car.
Police requested the driver of the car to turn herself in. Witnesses to the incident are also being sought by police.
On Wednesday police said the motorist had indeed turned herself in.