Argentina defender Rojo suffered a dislocated shoulder in the 1-0 derby defeat at Manchester City last weekend to give United manager Van Gaal another defensive headache.
Rojo visited a specialist on Thursday and Van Gaal has revealed that the former Sporting Lisbon man does not require surgery and should be back before the end of December.
He said at a media conference on Friday: "Marcos dislocated his shoulder but did it in positive way.
"We don't need to operate on him, which is a relief, but maybe with this injury it is very difficult that it shall not happen again.
"That is the problem. He saw a specialist who said the conserve way to heal is best. For him, it was positive. Always with these injuries, I cannot change the human body. Conservatively, less than six weeks out."
Van Gaal's side occupy 10th place in the Premier League ahead of Saturday's clash with Crystal Palace at Old Trafford and former United midfielder Paul Scholes stated that he expected the Dutchman to make more of an impact.
The former Netherlands coach knows his time at the club has not gone to plan so far, but is adamant United will turn the corner under his leadership.
He said: "I feel for the fans and also the board because they have belief in me, my staff, and my players. Thirteen points from 10 matches, you are not doing well, but we are in a process.
"As I have said from the beginning, even when we won five games in the US [during pre-season], the process shall take more than one year.
"It shall take three years, I hope, though that is dependent on lots of things. But I think we will make it happen, that we will win a lot of matches.
"I have the experience that people have great belief in what we are doing now, in the way we are playing football. When I am in the streets I am surrounded by very positive things, and when I'm in a car from United, there are lots of positive people.
"I'm feeling lousy for everyone that we have 13 points from 10 games. When I want to select the same line-up, I cannot. It's the same every week."
