The unexploded ordnance was found near Haugh Street at about 4.10pm on Thursday.
Police officers and an explosive ordnance disposal (EOD) team were called to the scene to deal with the device.
A police spokeswoman said: “Officers in Edinburgh were contacted after a possible unexploded ordnance device was discovered near Haugh Street at 4.10pm on Thursday, 5 August. A cordon was put in place. EOD attended and dealt with the item.”