South Yorkshire Police said 15-year-old Summer Lee Seymour died early on Saturday as a result of her injuries.
The incident happened at about 17:00 GMT on on Friday, on Haymarket at the junction with Castle Street . Police have appealed for witnesses.
A 17-year-old boy also suffered serious injuries and was taken to hospital, added police.
There were no passengers on board the bus at the time of the incident, said First South Yorkshire.
Spokesman Kevin Belfield said: "My thoughts are with everyone who has been affected by this tragic incident."
The cause of the incident is unknown, he added.
The driver of the bus has not been suspended, the company said.
A girl has died after two teenagers were in collision with a bus in Sheffield.