Four-year-old Chino the labrador was walking in the city’s Linn Park with owner Elizabeth Brydon when he suddenly jumped over the crossing’s wall.
The animal was taken to the vets in a critical condition, having suffered a collapsed lung and severe bruising.
Ms Brydon said: “It all seemed to happen in slow motion. I remember seeing him in mid-air, feeling utterly helpless.
“I saw him motionless at the bottom of the bridge and I thought he was dead. There was very little water in the river, so he fell straight onto the rocks below.
“When I didn’t see him moving, I thought we’d lost him.”
PDSA vets used X-ray images to reveal Chino had suffered serious chest injuries but had not broken any bones.
He was given painkillers and stayed at the surgery overnight, where he was monitored closely. The animal was then able to return home the next day, so he could recover more comfortably.
Chino is now said to be making a “remarkable” recovery, with Ms Brydon “over the moon”. She added: “He’s my miracle dog.”
Vet Susan Hermit said: “He is a very lucky dog not to have died that day.”
PDSA has launched its #SaveAStar, which asks for £5 donations to help carry out life-saving operations and provide care to suffering pets.