Halsey received the insulting messages, which made mention of his suffering from throat cancer, after overseeing United's 2-1 win at Anfield where he sent off Liverpool's Jonjo Shelvey.
Two tweets were sent out by unhappy Liverpool fans 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."
Halsey returned to refereeing in March 2010 and Professional Game Match Officials Limited said in a statement: "PGMO abhors any abuse of match officials whether that is in stadia or outside of it.
"Our main concern is towards Mark and his family, and as with all match officials, there is a backroom team who are there for them."