Ingimarsson sustained a hamstring injury in stoppage time of Saturday's 1-1 draw at Middlesbrough and now looks set for a few weeks in the treatment room.
McDermott told the club's official website: "We'll assess him and see how long he's going to be. We'll take care of him and he'll be back when he's right.
"He's a great pro, he played on for 20 minutes with the injury and he looks after himself perfectly, he will do all he can to get himself back playing as soon as possible."
Zurab Khizanishvili looks set to replace Ingimarsson in the starting line-up, while Matt Mills will be given the captain's armband in Ingimarsson's absence.
Kalifa Cisse is still building up his fitness following a thigh problem and is unlikely to figure, while Jem Karacan (hand), Noel Hunt and Chris Armstrong (both knee) remain on the sidelines.