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.

Waites thrashed Jeff Smith 7-1 in Sunday's final at Lakeside.
The 38-year-old from Huddersfield had an operation on a rotator cuff problem in February.
"I had six weeks without throwing a dart - that's painful in itself. Now I'm taking the world title back home," he told BBC Sport.
"It's hard trying to come back from an injury and trying to get yourself to practice. Sometimes, no matter what you do, your body won't react with it."
Waites, who added to his previous Lakeside success from 2013, continued: "This week, I've prepared myself to play for two hours in a session and it's so difficult to do. My shoulder and my body wasn't happy with that.
"After I played Glen Durrant [in the quarter-finals on Friday] I ended up going to sleep at half past eight."
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Waites, who was the ninth seed, is the eighth man to win the BDO title on more than one occasion.
He raced into a 5-0 lead in the final against unseeded Canadian Smith, 40, and eventually wrapped up a comfortable victory.
"It's not really sunk in yet," said Waites, who will return to his job as a carpenter on Tuesday.
"I can't believe it was over so quickly. I set myself up for it being a really tough game and Jeff, although he pushed me a little bit, didn't take his opportunities.
"I took my opportunities when I got them and I was taking sets."

The 22-year-old has played for the Auckland Blues Development side as well as Northland in the ITM Cup.
"He is a young prop who can play on both sides of the scrum and I believe he has huge potential," said Connacht coach Pat Lam.
"I know he will continue to thrive and develop in a full-time professional environment."
He added: "I first saw Dominic as he came through the Auckland Schools system and played for the Blues U18s in New Zealand.
"We're looking forward to getting him over for the pre-season as we build towards the start of a new season in both the Pro12 and European Champions Cup."
Robertson-McCoy is Irish qualified through his grandfather, who hails from Mowhan in Co Armagh.
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.
[NEXT_CONCEPT]
Scott Waites was delighted to clinch a second BDO world title, admitting it seemed "a million miles away" following shoulder surgery last year.
[NEXT_CONCEPT]
Pro12 champions Connacht have signed  Irish qualified tight-head prop Dominic Robertson-McCoy from New Zealand.