Van Persie, who has scored 10 goals for United this season, turned his right ankle in the closing stages of the 2-1 defeat to Swansea last Saturday and left the Liberty Stadium on crutches.
Scans have shown the injury is ‘not heavy’, according to Van Gaal, but he still expects the striker to be out of commission for a number of weeks.
The United boss said: “He is injured. He is the only injured player I have, so we change (Michael) Carrick for Van Persie.
“He has an ankle problem. I don’t think it’s very heavy but an ankle problem takes a long time. It’s not one week or two weeks but we have to wait and see.”
Radamel Falcao is expected to deputise in the United starting XI against Sunderland on Saturday with James Wilson ruled out with a dead leg.
Van Gaal said: “The possibilty is higher for somebody else because when a striker is away another striker has to play.”
United go into the game in fourth place and asked how he would feel if they finish below that this season Van Gaal said: ‘It would be a big disappointment. When you start a season with that objective then you are occupied with that. But we are still there in the top four. I don’t know why we are talking about this.
“We are still in the FA Cup. I am pleased with the results but not with a lot of the performances of my team.
“But always we are getting better despite all the injuries that we have suffered. Despite all the criticism of our defence we don’t have many goals against us. We are not unhappy but we could have had better results.
“When you see our matches we are mostly the better team but the better team is not always winning.”