An off-duty inspector found the girl in Grange Lane, Lye, near Pedmore Technology College, Stourbridge.
Police are seeking a light grey or blue vehicle in connection with the crash.
Sgt Steve Newbury said: "It's shocking to think someone could leave a child seriously hurt in the street, drive off and make no effort to get her medical treatment."
Updates on this story and more from the Black Country
He added: "Clearly this is distressing at any time for the girl's family, but to happen just days before Christmas is truly heartbreaking."
The girl suffered a fractured skull and internal injuries in the crash, thought to have happened just before 22:00 GMT on Thursday.
A spokesman for West Midlands Ambulance Service said it was clear "the 15-year-old had multiple serious injuries" and there was no car at the location.
"She was treated at the scene by ambulance staff before being taken to Russells Hall Hospital."
Her condition on arrival there was described as critical but stable.

The 35-year-old batsman will link up again with his ex-Black Caps team-mate Daniel Vettori, who was appointed Middlesex's Twenty20 coach on a three-year deal in December.
McCullum worked under Vettori at Big Bash side Brisbane Heat this winter.
Meanwhile, James Franklin, 36, has been made full-time captain in the County Championship and the One-Day Cup.
Franklin took over the captaincy on an interim basis last season following an injury to Adam Voges and helped steer the club to their first Championship title since 1993.
"It's a very exciting time for the club, getting Brendon back again after his stint with us last year," Franklin told BBC Radio London.
"He's one of the best captains in world cricket of the modern age so it's going to be exciting for players to work with him.
"And Dan being on board as the Twenty20 coach, I think it shows how progressive the club are looking at things.
"To be able to get in a coach of his calibre is hugely exciting."
Last season's T20 Blast captain Dawid Malan, 29, has been named vice-captain in that format and will lead the side when McCullum, who has re-signed for nine group games, is unavailable.
A 15-year-old girl has been critically injured in a suspected hit-and-run in the Black Country.
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Former New Zealand skipper Brendan McCullum has been named Middlesex captain for this season's T20 Blast.