Dorgu suffered a rollercoaster of emotions on Sunday afternoon when he first gave the visitors a 2-1 lead with a stunning long-range goal before being taken off with an injury just half an hour later.
The Danish international United defender immediately felt his hamstring when he hit the turf after chasing a loose ball. He was replaced by Benjamin Sesko.
United's interim manager, Michael Carrick, said in the post-match press conference that "he came off with hopefully a little bit of cramp, but hopefully it's nothing worse."
"He ended up coming off, but I think it just shows what he put in with his performance. But yeah absolutely delighted for him, just hope he's not too bad.
"At this stage, it's hard to tell. We'll just have to wait and see but for sure we're hoping that it's not too bad.”
Dorgu is now expected to be out for 10 weeks, meaning he will miss the club's next eight games.
He is not expected to be back until after the international break in March, when United face Leeds United on April 11th.
Denmark will play the play-off semi-final against North Macedonia on March 26th in the Parken Stadium in Copenhagen. Should they win that match, they will face the winner of the Czech Republic and Ireland in the play-off final.
United have yet to confirm the news on the club's website. Dorgu has provided three goals and three assists in 22 Premier League games.