The Denmark wing-back has suffered a hamstring injury in the past week.
Carrick said, "We’re working through it. It’ll definitely be a number of weeks, it will be a considerable period of time. He’s not going to be back in the next two or three weeks. To be more exact is a little bit difficult at this moment.”
Asked if it could be "10 weeks" before United fans see Dorgu again, Carrick continued: “It could possibly, we’re working through it. Certainly looking forward to getting him back as quick as we can and getting on the pitch long before the end of the season.
“It’s a blow, it’s always a blow when you lose players and they can’t be involved, and we can’t choose them. Especially when you’ve had an impact like Patrick did over the last few weeks. Just finding that next level.
"Unfortunately, football throws things up, there’s up and downs. For this short period of time, he’s disappointed, he wants to be fit. But he’s going to have a career for the next 10 or 15 years and hopefully this is just a little moment for him.
"Coming off the back of the huge positive he’s just had, I think when he comes back, he’ll be even stronger again.”