The 47-year-old pedestrian suffered head injuries in the collision in Gorgie Road at around 9pm, but police said they were not life-threatening.
The Scottish Ambulance Service arrived treated him at the scene before transferring him to the Edinburgh Royal Infirmary at Little France.
It is understood he sustained multiple skull fractures, though it is not known if he has been transferred for treatment at a specialist unit.
A spokesman for the Scottish Ambulance Service said: “We received a call to say a male had been knocked down by a bus.
“We arrived on the scene to find a male with serious head injuries and he was taken by ambulance to accident and emergency.”
This morning, emergency services were waiting for an update from NHS Lothian about his progress.