Striker Fryatt is battling an Achilles problem whilst young defender Dudgeon will require surgery on a troublesome knee injury with manager Steve Bruce confirming the likely lengthy absences.
"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."
The Tigers currently sit sixth on the Championship table with 22 points after 13 matches.