Ashya King – who has a brain tumour – was taken by his parents from a hospital in Southampton on Thursday.
The family – including Ashya's six siblings – were last seen on a ferry bound for France.
Officers say they need to find him urgently and fear the battery for his lifesaving feeding tube has already run out of power.
According to Assistant Chief Constable Chris Shead there have been several sightings of the family's car.
