The object was found underneath a house on Corstorphine Rd, at about 7.40am, a police spokeswoman said.
There is a scene guard in place and the Explosive Ordnance Disposal team are due to attend later today.
The object was found by a resident of the house, the spokeswoman said.
"None of the nearby residents have needed to be evacuated at this stage."
Police were unable to confirm how old the suspected munition was.