The BBC pundit praised the Newcastle United striker's passion but has warned him about keeping it in check.
Indeed, Mitrovic showed off his passion for the cause just seconds after coming on as a substitute against Southampton on Sunday afternoon - but Murphy says the last thing anyone needs is for a 'bit of stupidity' to get them sent off.
Mitrovic, a £13 million arrival from Anderlecht this summer - fee as reported by the BBC - will endear himself to the Newcastle fans, according to the pundit, but will have to keep his aggression in tow.
Murphy said on Match of the Day: "He comes with a good reputation but this [the tackle Mitrovic made just 16 seconds after coming on] is ridiculous.
"Steve McClaren will have a chat with him, for sure, because the last thing you need in the Premier League is for a bit of stupidity to get you sent off. His passion and endeavour will endear him to the supporters but he can’t be doing stupid tackles like that."
As Opta stats rather alarmingly show, Mitrovic committed as many fouls as any other Newcastle player did in 90 minutes against Southampton... in just 15 minutes.
The 20-year-old was reckless in the tackle and, according to McClaren, could well have been sent off.
Of course, the Serb was brought to St James' Park partly because of his aggression and, should it be kept in check, there will be little to worry about for the Magpies. But it's certainly worth taking Murphy's warning into consideration - and for McClaren to have the odd word with his young striker.