Speaking at his press conference on Friday, Carrick confirmed the injury would keep Dorgu out but stressed that the club are still evaluating the full extent of the damage.
"Pat, unfortunately, he's going to be out for a period of time. We're still working through how long that's going to be," Carrick said.
"We'll have to see, it's disappointing, he's had such a big couple of weeks, Pat. We weren't sure whether it was a little bit of cramp or whether it was something a little bit more serious and at the moment it looks a little bit more on the serious note.
"So, it'll be a few weeks for that. How many weeks? We'll have to wait and see. So, that's disappointing for all of us really, and for Pat, he's in such a good place, but unfortunately it is part of football and it's something we've got to work through and get him back as soon as we can."
United are already preparing for life without Dorgu in the short term, with the wing-back set to miss Fulham’s visit to Old Trafford this weekend. Matthijs de Ligt will also be unavailable for that fixture, further limiting Carrick’s defensive options.
There was more positive news on the fitness front, however, with Joshua Zirkzee returning to training and potentially in contention to feature for the first time under Carrick.
"Josh is back training this week, which is good news," Carrick added. "He's been out for a short amount of time, but first kind of training with us since we've been here, so that's great to have Josh back."
United will continue to monitor Dorgu’s recovery in the coming weeks, with the club hopeful of reintegrating him as soon as medical staff allow.