The Scotland international was left with ligament damage as well as three wounds which required stitching after a challenge by Hamza Choudhury.
Newcastle face Watford tomorrow and Bruce has said if they win it will be a ‘wonderful start’ to the season.
Bruce said: “It’s not great news. We think he’s going to be maybe two months, eight weeks. There is ankle ligament damage too, bone bruising, cuts. The kid, as I said to you the other night, was a mess.
“Thankfully it’s not six months, but it’s bad enough when it’s the best part of eight weeks.”
Bruce described Choudhury’s challenge as a “horror tackle” in the immediate aftermath of the game, and urged the midfielder to learn from the experience.
He said: “These tackles are the ones that damage you. Let’s hope the young lad learns from it because he’s a good player, the kid.
“But obviously, it doesn’t help us and Matt in particular, who’s going to miss at least a couple of months.”