Austria international Sabitzer joined United from Bayern Munich in January on a short-term deal until the end of the season. He has scored three times in 18 appearances and won the League Cup in February.
"Marcel Sabitzer has suffered a meniscal injury which will, unfortunately, rule him out for the remainder of the season," United said in a statement.
"Everyone at the club is disappointed to lose Marcel's services, as we strive for a strong finish to our season... and we appreciate his contribution to our progress so far."
Sabitzer made 24 appearances for Bayern this season before joining United. He has won 69 caps for Austria.
United travel to Bournemouth on Saturday before hosting Chelsea and Fulham. They will take on Manchester City in the FA Cup final at Wembley on June 3rd.
