Police have arrested a 29-year-old man on suspicion of causing serious injury by dangerous driving and failing to stop following the hit and run on Wednesday evening.
The crash involving the girl and a motorbike happened in Low Poppleton Lane, York, at around 5pm.
The girl was rushed to Leeds General Infirmary with serious injuries.
Police launched a desperate appeal to trace the biker.
The motorcycle involved - a grey Kawasaki - has still not been found, but police say it will have extensive damage to the front end and headlight.
A North Yorkshire Police spokesman said: "Officers investigating a collision involving a 12-year-old girl and a motorcycle in York have arrested a man.
"A 29-year-old York man was arrested at 8pm yesterday on suspicion of causing serious injury by dangerous driving and failing to stop. He remains in custody at this time.
"The girl is in a critical condition in hospital. Her family are with her, and are being supported by specially-trained police officers.
"Officers have had a good response to their appeal for information, and are continuing to urge anyone who witnessed the collision or the motorcycle leaving the scene to contact North Yorkshire Police. They also want to speak to anyone who may have footage of the incident on dashcams, or home- or business-based CCTV systems.
"At this time the motorcycle involved has not been recovered. It is believed to be a grey Kawasaki with extensive damage to the front end and headlight. Anyone who knows where the bike is asked to contact North Yorkshire Police as a matter of urgency.
Anyone with information can call North Yorkshire Police on 101, quoting NYP-12062019-0335.