No details of the incident have been released but police have confirmed that the Cowgate, between West High Street and Catherine Street is currently closed to all vehicles and pedestrians.
As a precaution, a number of residents in nearby properties have been evacuated from their homes.
Police Scotland added that there is currently no threat to the wider public.
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The incident happened in the early hours of Monday at a Santander branch on Cowgate, Kirkintilloch.