Officers were called to Kenton Road with the junction of Claremont Avenue, Brent, at 7.40am on August 26, to reports of a collision between a car, a red Ford Focus, and two pedestrians.
London Ambulance Service and the London Air Ambulance attended the scene.
Medics treated a two-year-old boy and his 59-year-old grandfather. Both were taken to an east London hospital.
The child’s condition is described as life-threatening. The man is described as non-life threatening.
Next of kin are aware.
A 22-year-old man was arrested on suspicion of causing serious injury by dangerous driving.
He was taken to a north London police station where he was bailed to a date in October.
Officers would like to hear from anyone who may have witnessed the collision to contact the Met’s Serious Collision Investigation Unit at Alperton on 0208 991 9555 or the police non-emergency line on 101.