The discovery was made around 12:45 p.m. by a member of the public.
An Explosive Ordnance Disposal (EOD) team is en route to the incident from Faslane Naval Base.
HM Coastguard has been alerted and part of the beach near the skatepark has been closed to the public while the device is investigated.
Just before 4 p.m., the coast guard then closed the beach completely and closed the parking lot.
A small crowd that had gathered was moved about 100 meters back and a cordon was put in place.
It is believed that a WWII aircraft was spotted among the rocks on the shore when the tide was low.
A spokesperson for HM Coastguard said: “We were alerted by a member of the public that they had spotted what they believed to be ammunition.
“We are currently investigating.”