A member of the public walked into Greyfriars police station at 4.10pm to hand in the old-looking device.
It is understood it had been discovered buried elsewhere in town.
“It is believed to be an old unexploded hand grenade,” said a police spokesman.
Officers called the army bomb disposal squad and, as a precaution, cordoned off the streets surrounding Greyfriars.
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Union Street is closed at Midland Road and Alexandra Place, Hassett Street and Priory Street are all off limits.
The bomb disposal experts are now on their way.