The news is another low point for Van De Beek in his Manchester United career.
At no point in his time at Old Trafford has the 25-year-old been a regular starter.
Van De Beek has only made 10 appearances in all competitions this season after spending the second half of the last campaign on loan at Everton.
The Netherlands international picked up the injury at the start of this month against Bournemouth in the Premier League.
"On the long term it is looking really good, he will be back for the start of pre-season," said United manager Erik ten Hag.
"The rest of the season he is out."
"I think everyone's thoughts are with him," added Ten Hag. "It is terrible when you are in a season and you get a bad tackle, a bad injury.
"It is always really disappointing and thoughts, feelings are with the player. You express that, our group did that really well, and we are now happy his knee in the long term is good.
"In the same moments, mixed feelings. Disappointment he is out of this season.
"The players are feeling we are building something good and we want to be part of it and everyone wants to be part of it."
Reacting to the news on Twitter, Van De Beek wrote: "I am really disappointed that the season is over for me.
"After successful surgery, it’s time to start my recovery process and will do everything to come back stronger for this club.
"Thank you all for the lovely messages, they mean a lot to me and my family."
Van De Beek joined Man United from Ajax Amsterdam in the summer of 2020.
