Mr Murphy, who represents Newry and Armagh, received the telephone threat at his Newry constituency office on Tuesday.
The caller claimed to represent the UVF. He told Mr Murphy he would be shot in his home.
The senior Sinn Fein politician said he reported the incident to police.
"Considering the antics of the UVF in Belfast of several months now we took the threat seriously," he said.
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? email@example.com