A man in his 40s has been arrested in relation to alleged “malicious” comments made on social media.
It is understood he is being questioned about making threats against Health Minister Robin Swann.
Police confirmed the man had been arrested in the Newtownards area on Thursday afternoon.
Steve Aiken, leader of the Ulster Unionist Party, said the threats against the health minister were “absolutely despicable”.
“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,” said Mr Aiken.
“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.