A man in his 40s has been arrested in relation to alleged “malicious” comments made on social media.
It is understood he was questioned about making threats against Health Minister Robin Swann.
Police confirmed a man had been arrested in the Newtownards area.
Steve Aiken, leader of the Ulster Unionist Party, said the threats against his party colleague the health minister were “absolutely despicable”.
Mr Aiken added: “The torrent of abuse and lies which Robin has had to put with from some anonymous trolls and others who should know better has been abhorrent.
“This isn’t the first time that Robin has had threats of physical violence made against him, but it should be the last.
“He took on a job which no-one else wanted and he has committed long days and nights making difficult decisions, working with his colleagues in the Department of Health and the NHS, to protect the public during a global pandemic.”
Mr Aiken said the health minister has been “verbally attacked” with threats of physical violence made against him and his family.
“Nobody should have to put up with that,” he added.
Mr Aiken called on social media platforms to take responsibility for the threats by banning anonymous trolling online.
“If the social media giants aren’t prepared to act voluntarily, then Government needs to intervene,” he said.
“I commend the PSNI who have acted swiftly to make an arrest,” he said.
On Thursday Mr Swann said that in regard to “personal abuse that I received last night” he said he believed it was necessary to inform the police.
He said he believed a person had been arrested “because of the nature of the threats that were made”.
The Health Minister, who is also an Assembly Member for North Antrim, added: “I would rather people direct that frustration and anger at me as minister, than at the health service workers or at those front-line workers.
“If a level of frustration is targeted at me rather than them, I will accept that.”