Police Scotland said the move came after a joint operation which has also involved the Police Service of Northern Ireland and the Security Service.
It focused on the activities of individuals sympathetic to dissident Republicanism but who are not affiliated to any specific group.
Police Scotland Assistant Chief Constable Ruaraidh Nicolson, Organised Crime, Counter Terrorism and Safer Communities, confirmed they were arrested at several locations under S41 of the Act on suspicion of committing various offences.
He added: "Police Scotland has led the operation which has involved a number of officers, including specialist units, and public safety has been a priority throughout.
"We are confident as a result of these arrests there is no risk to the public. It would be inappropriate to comment further at this stage."
Details of how many arrests were made have not been made public.