Police Scotland said a man, whose age has not been given, was arrested under the 2000 Terrorism Act.
The development was revealed a day after five people with alleged links to dissident republicanism appeared in court charged with terrorism offences and conspiracy to murder.
Anton Duffy, Martin Hughes and Stacy McAllister, from Glasgow, Paul Sands, from Ayr, and Edward McVeigh, from Portpatrick, Dumfries and Galloway, were arrested last Wednesday in the operation led by Police Scotland and involving the Police Service of Northern Ireland and the security service.
No other details about the arrest have been released.
Duffy, 39, Hughes, 34, Sands, 30, McVeigh, 26, and McAllister, 27, appeared separately in private at Glasgow Sheriff Court yesterday and were charged under Section 5 of the Terrorism Act, which covers the preparation of terrorist acts, and conspiracy to murder.
All five made no plea or declaration and they were remanded in custody.
The suspects were charged with plotting to murder former Loyalist chief Johnny "Mad Dog" Adair, it was reported.
Following the arrests last week, Police Scotland said the operation focused on the "activities of individuals sympathetic to dissident Republicanism but who are not affiliated to any specific group".
The court appearances happened amid heightened security with armed officers inside and outside the court.