Fryatt has been struggling with an Achilles problem since the beginning of the season, while former Manchester United defender Dudgeon injured his knee in September.
"I think the decision as far as Joe is concerned has been made. It's a horrible operation that he's going to have and it's a real shame. Matty Fryatt looks as though he's going to have one as well and that's two big injuries," Bruce told the club's official website.
"With Joe, he's damaged the bottom of his knee and it's a chondral defect which is basically a hole in the back of his knee. We wish them both a speedy recovery, but I think it will be next summer before we see the two of them if I'm being honest."
Hull currently sit sixth in the Championship table.