Hobbs was forced out of the Tigers' fourth straight defeat when going down to Coventry at the weekend, while the club are also waiting to learn the full extent of an injury to a third defender, James Chester.
Manager Nick Barmby said of centre-half Hobbs: "It doesn't look great and it looks like there is a bit of damage in there.
"I'm not going to diagnose his injury, but he'll be out for the rest of the season."
Dudgeon has also been ruled out for the remainder of the campaign with a hamstring injury sustained in the recent defeat at Portsmouth, while Chester sustained a hamstring during the week.
Barmby added: "Joe will be out for three months. James has a hamstring problem and we don't know how long he's going to be out for yet, but I certainly won't be rushing him because I'm more concerned about his health. He's had a scan and there's a slight tear, so it all depends how he responds to treatment."