Police believe the vehicle struck the 19-month-old just before midday at Sarehole Mill in Billesley before emergency services arrived and took the boy to hospital with a “critical head injury”.
A 30-year-old man and a 26-year-old woman have been arrested on suspicion of causing serious injury through dangerous driving and are in police custody.
Officers have seized a van for forensic examination.
Inspector Steve Radford said: “We believe the collision happened on grassland just off Wake Green Road – the child is very poorly in hospital and we await an update on his condition.
“I’m keen to hear from anyone who was in Wake Green Road or the immediate vicinity and may have witnessed the collision or heard anything that may assist our investigation.”
:: Anyone with information can call police on 101 quoting the reference 1016 and the date 13 July.