Some people were taken aback when the Northern Irish presenter commented on Liverpool goalkeeper Pepe Reina's "lame headbutt" on Newcastle defender James Perch on Sunday which led to the Spaniard being dismissed.
Murray asked pundit Mark Lawrenson: "When you get sent off for that type of lame headbutt, do you regret not sticking the head in anyway?" and some viewers interpreted the comments as Murray condoning more aggressive behaviour.
In a tweet republished by the Daily Mail, Carl Waring said: "Cannot believe what Colin Murray has just said on MOTD 2 about headbutting. Just what do the BBC see in him as a presenter?"
Another viewer, Hayley Usher added: "Colin Murray is a disgrace for saying that. Basically inciting violence on the pitch."
The BBC then apologised for the comment by saying: "We're sorry for any offence caused."
Murray is a big supporter of Liverpool and had five stars tattooed on his arm when the club won the European Cup for the fifth time in 2005.
He has been hosting MOTD2 since 2010 when former presenter Adrian Chiles left the BBC for ITV.
The Reina-Perch incident caused a major debate amongst football fans with many criticising Perch for his dramatic fall to the ground after being confronted by Reina.
However, former referee Dermot Gallagher told Yahoo! Eurosport that the decision to send off Reina was the correct one.