The suspect was arrested around 4pm after witnesses of the incident phoned the police and emergency services.
The alleged victim is believed to have sustained non-fatal injuries.
Several officers and two vehicles were at the scene of the arrest outside a shop on The Royal Mile.
It is believed that one of the witnesses who phoned for assistance was Cllr Gordon Munro.
A spokesperson for Police Scotland said: “Police received a report of a man having been assaulted at Crichton’s Close Edinburgh. A man has been taken to hospital. Enquiries are continuing.”
Join our Facebook group Our Edinburgh to share images and news from and around the Capital