The Austria international joined from Bayern Munich in January on a short-term deal which runs until the end of the campaign.
But after suffering meniscal damage, he will not be able to recover in time to play a part in any of United's final three Premier League games or the FA Cup final next month.
“Everyone at the club is disappointed to lose Marcel’s services, as we strive for a strong finish to our season,” United said. "
Sabitzer has made 18 appearances and scored three goals since his arrival.
He was also part of United's Carabao Cup-winning team at Wembley in February.
It was not clear if the injury would play a part in United's decision-making over whether to try to sign him on a permanent deal.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)
Short link: