The incident happened shortly before 4pm yesterday in the Bingham area of the Capital, and resulted in one man, aged 31, being taken to hospital.
A second man, aged 57, was treated by paramedics at the scene.
Witnesses reported a heavy police presence in the area, along with the Scottish Ambulance Service following the serious assault.
Police have confirmed that an investigation is underway.
A Police Scotland spokesperson said: “Around 3.55pm on Wednesday, 21 July, we received a report of a serious assault on Bingham Medway in Edinburgh.
“Emergency services attended and two men were found to have suffered injuries.
"One of the men, aged 31, was taken to Edinburgh Royal Infirmary for treatment to serious injury, the other man, aged 57, was treated by the Scottish Ambulance Service.
“Enquiries are ongoing.”