The car mounted a pavement within the grounds of Maidstone Hospital, in Barming, at about 14:40 BST on Tuesday, police said.
The woman, in her 90s, was taken to a hospital in London, where she was later pronounced dead.
Police have appealed for witnesses to the crash, which happened near the hospital's birthing centre.
A woman in her 90s who was in a wheelchair when she was hit by a car outside a hospital has died.