Emergency services raced to the scene near the Aldi store following reports of an assault at around 5.15pm.
An eyewitness, who did not wish to be named, told the Evening News a man had been “stabbed”.
The man has been taken to the Edinburgh Royal Infirmary for treatment.
Officers remain at the scene with Gilmerton Road closed between Moredunvale Road and Ellen’s Glen Road.
A Police Scotland spokesman said: “At 5.15pm on Sunday 14 April 2019 police in Edinburgh responded to a report of a person having been assaulted on Gilmerton Road. The person has been taken to Edinburgh Royal Infirmary.
“Officers remain in attendance and road closures are in place on Gilmerton Road between Moredunvale Road and Ellen’s Glen Road.”