Fryatt has been struggling with an Achilles problem while Dudgeon took a knock to his knee in the defeat at Leicester in September.
And Hull boss Steve Bruce has confirmed both players will need surgery on their respective injuries and are likely to miss the rest of the season.
"I think the decision as far as Joe is concerned has been made," he told the club's official website.
"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.
"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."