The girl was with her parents and a younger brother when she attended St Mary's Hospital in Paddington, London, at about 17:40 BST on Sunday.
But the family left two hours later before the girl, who police believe is diabetic, could receive treatment.
Police said the girl could fall into a coma if not treated immediately.
A Scotland Yard statement said: "The girl was initially seen by medical staff and her parents informed them that their child's name was Mashael Aldosari.
"Detectives are unsure if this is the child's real name as the family provided a false address to staff."
The family told medical staff they travelled to the UK in order for their son to receive hospital treatment.
Police said they have "established that this is may not be the case".
Mashael is described as being less than 5ft tall with long straight black hair. She was last seen wearing a grey top, leggings and light-coloured shoes.
Detectives believe the family could be from Kuwait.
Police are appealing for help locating a sick nine-year-old girl who went missing after being taken to hospital in need of urgent medical care.