She was taken to hospital, where her condition is described as “serious but not life-threatening”.
The driver of the van stopped further up the road, then left the scene.
Police said inquiries were ongoing to trace the vehicle and driver.
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Road policing Constable Scott Smith said: “I would urge the driver of this black van to come forward as quickly as possible. They will be aware they’ve been involved in a collision and are likely to have damage to their vehicle.
“I am also appealing to anyone who was on the A82 around the time and saw what happened to get in touch. If you have dashcam footage of the area please review this and bring anything significant to our attention.”
Police Scotland have asked anyone with information to contact them on 101 quoting reference 2307 of November 24.