The boy, 16, was riding on Brantingham Road, Elloughton, when he was hit from behind and knocked down by a car on Friday night.
He is in a critical condition at Hull Royal Infirmary after the driver failed to stop, Humberside Police said.
A 63-year-old man is being held in connection with the incident.
A man has been arrested after a teenage cyclist suffered life-threatening injuries in a hit-and-run in East Yorkshire.