The incident happened outside the multi-storey car park in Leopold Street at 9.35pm on Wednesday.
A girl of primary school age also suffered serious injuries, Kent Police said. She has been taken to a London hospital for treatment.
A man in his 40s and a boy of primary school age sustained minor injuries.
A 30-year-old man from Ramsgate was arrested on suspicion of causing death by dangerous driving and leaving the scene of a collision. He is receiving hospital treatment for minor injuries.
Enquiries into the incident are being carried out by officers from the Serious Collision Investigation Unit who are keen to hear from any witnesses, local businesses with CCTV evidence or drivers with relevant dashcam footage.