Halsey received the insulting messages on the social networking site Twitter, referencing his battle with throat cancer in 2009, after taking charge of Liverpool's contentious 2-1 defeat against Manchester United.
And the 51-year-old has asked the police to investigate the matter, a Professional Game Match Officials Limited (PGMOL) spokesman confirmed to Press Association Sport.
The abusive tweets come just days after the Director of Public Prosecutions said new guidelines for prosecutors on social media cases will be issued in the wake of a number of growing complaints.
Last week a Welsh Premier League footballer who posted an abusive message about Olympic diver Tom Daley was not charged because the message was "not so grossly offensive that criminal charges need to be brought", Keir Starmer said.
Halsey made two controversial decisions on Sunday, both of which went in favour of Manchester United, sending off Liverpool midfielder Jonjo Shelvey before awarding United a penalty, which was scored by Robin van Persie.
Two tweets were sent out by disgruntled Liverpool supporters following the game, both of which were met with outrage from other Twitter users. One post, from an account named @johnwareing1, read: "I hope Mark Halsey gets cancer again and dies'' while another from @lfcjohn259 read: "Mark Halsey should've died of cancer."
The post from @lfcjohn259 was deleted and the @johnwareing1 account was removed completely but the national secretary of Prospect, Alan Leighton, expressed his union's disgust regarding the tweets in a statement to Press Association Sport.
His statement read: "Prospect wholeheartedly condemns the unacceptable abuse aimed at Mark Halsey on Twitter. The comments made by a very small minority will be seen as beneath contempt by all decent people."
The abusive Twitter users were also condemned by PGMO, which provides referees to the Premier League, offering support to Halsey if and when it is required.