Devon and Cornwall Police say he was walking along Merafield Road near Gables Farm when he was struck at about 10.15am on Friday.
The pedestrian, in his 20s, was taken to Derriford Hospital with “serious leg, hand and facial injuries” which are not thought to be life-threatening.
The male driver was also taken to hospital, but their injuries are not known at this time.
All roads have now reopened.
A force spokeswoman said: “Police responded to a serious collision in Plympton involving a car and a male pedestrian.
“Emergency services were called at 10.15am on Friday, November 15, after a car hit a man on Merafield Road.
“The pedestrian went over the railings of the bridge, down a bank towards the A38.
“It is believed he ended up at the bottom of the bank near the carriageway.
“The pedestrian, a man in his 20s, has sustained serious leg, hand and facial injuries.
“He was taken to Derriford Hospital by ambulance. These injuries are not described as life-threatening.
“The male driver of the car has also been taken to hospital - their injuries are not known at this time.
“The A38 was closed in both directions for a short time for the air ambulance to land.
"All lanes now open.
"Officers have conducted an examination of the scene of the collision in Merafield Road.
“This road reopened at 1.35pm.”