The 21-year-old woman was walking across a pedestrian crossing close to Ryelands Park in Lancaster when she was struck by a van.
She suffered serious injuries and was taken to the Royal Preston Hospital where she remains.
The van, a blue Ford Transit style, made off from the scene towards Morecambe and was found abandoned a short time later in the Fairhope Avenue area.
Police were called by the ambulance service shortly after 3pm today to the crash in Morecambe Road.
It is believed there were two people in the van, described as white men, possibly wearing white or light coloured tops.
Enquiries are on-going to trace the individuals and police are appealing for anyone with information to come forward.
Detective inspector Andy Ellis, of Lancaster Police, said: “This was a significant collision which has left a young woman with some serious injuries.
"We are actively seeking the driver of the transit van and anyone else who was in the vehicle at the time of the collision and I would appeal for anyone who saw the collision itself or the van either prior to or following the collision to get in touch.
“This collision happened on a warm afternoon close to a park and I’m sure there were many people out and about who saw what happened.”
Anyone with information should contact police on 101 quoting log number 0873 of August 21st or independent charity Crimestoppers on 0800 555 111.