A man has been cautioned after "threatening and offensive comments" were made to Health Minister Robin Swann, the police have said.
The comments, which were sectarian in nature and targeted Mr Swann's son, were made on social media on 3 April.
Supt Darrin Jones said police had administered an adult caution to a 26-year-old man.
The comments were condemned by political leaders across Northern Ireland.
Deputy First Minister Michelle O'Neill had described the threats against the former Ulster Unionist Party leader as "disgraceful".
First Minister Arlene Foster said they were "vile and disgusting, especially at a time when we are focused on protecting life and getting Northern Ireland through Covid-19."
SDLP leader Colum Eastwood described them as "vile sectarian abuse and threats".
UUP leader Steve Aiken described the threats received by his party colleague as a "disgusting attack on someone who is doing their very best for everybody in Northern Ireland".
Mr Swann has not commented on the matter.