Laurance Price suffered a broken leg in the accident in Palmers Green, north London.
Laurance's mother, Celia, had just dropped her daughter Flora, six, at the school when the car, driven by a learner, left the road. The buggy was dragged under the car for several feet before it crashed into a garden wall.
An eyewitness said: 'The car just veered off the road and on to the pavement. Fortunately it wasn't going very fast. It's amazing that the child wasn't killed. I thought the worst when the buggy went under the wheels.
Last night Laurance was being treated in Chase Farm Hospital, Enfield. Mrs Price, of Palmers Green, was treated in the same hospital for shock.
A police spokesman said: 'We are investigating the accident. The driver and instructor were uninjured, though shaken. We don't know at this stage what caused the car to leave the road.Reuse content