It is understood the man, who is aged in his 40s, was arrested in Newtownards, Co Down over the allegations which centre around social media.
A PSNI spokesman said: “A man in his 40s has been arrested in the Newtownards area this afternoon in relation to malicious comments made on social media yesterday.”
In April a 26-year-old man was arrested in Ballymena, Co Antrim after “threatening and offensive comments” were made against Mr Swann on social media.
Ulster Unionist Party leader Steve Aiken condemned the threats made against his party’s minister.
“This isn’t the first time that Robin has had threats of physical violence made against him, but it should be the last,” he said.
“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, the likes of which we haven`t faced in 100 years.
“He has been verbally attacked, threats of physical violence made against him and his family, and attempts made to undermine his good character.”
