The former Hull KR forward sustained the injury early in the second half but went on to play the rest of the game, according to his coach Chris Chester.
Trinity will also be without second rower Matty Ashurst for Saturday's trip to Warrington Wolves after he sustained a calf injury in the same game while fellow back rower Dean Hadley is battling to overcome a shoulder problem.
"Mitch broke his hand in two places early in the second half but, being the guy he is, he ended up staying on and playing the rest of the game," Chester said.
"He needs an operation to have a plate put in so he will probably miss four or five games. He's been playing well so we'll miss him but it gives an opportunity to the rest of the squad and Keegan Hirst will probably get some more game time."
Chester says he is likely to bring in back row forwards Jordan Crowther and Mikey Sio for the game against the Wolves, along with full-back Max Jowitt, yet to play this season due to the presence of veteran Scott Grix, who has made an impressive start to his second spell with the club.
"Max has been very professional," Chester said. "He's learned a lot from Grixy and had a few games out on dual reg. He's obviously been disappointed but, when Grixy is playing so well, it's difficult not to play him every week. Hopefully if he gets an opportunity this week, he'll take it with both hands.
"I'll try to rotate this week because this is generally the game that catches you out over Easter from a fatigue point of view so it's important we bring some fresh guys into the squad.
"Grixy has played every minute of every game and he's not getting any younger. We've got to manage him over the next few weeks but we'll decide on Friday the make-up of our team.
"I was going to rest him on Monday but he was adamant that he wanted to play and put a few wrongs right from the game at Castleford."
Chester will also recall Australian half-back Sam Williams after resting him against Wigan.