It happened over a week ago, but has just been reported to police.
A 28-year-old man was involved in a collision with a car in the area of Burcot Lane and Drayton Road on Sunday 26 May.
He suffered a severe leg injury and was taken to the John Radcliffe Hospital, where he remains.
Police say the vehicle didn't stop at the scene.
Officers are keen to speak with anybody who left the Oxford Water Park between 5pm and 6pm, who may have seen what happened.
Investigating officer PC Andy Wickens of the Joint Operations Unit for Roads Policing based at Abingdon, said: "I would like to speak to anybody who may have seen this incident or saw two pedestrians walking in the area to contact police.
"I am also making a direct appeal to the driver of the car involved to get in touch to help with the investigation."