English centre back Holding, who has played 10 league games for Arsenal this season, left the pitch on a stretcher during the first half of the match with United and is set to undergo surgery in the coming days.
"Further to the injury sustained during our match at Manchester United on Wednesday night, we can confirm that Rob Holding has ruptured the anterior cruciate ligament of his left knee," Arsenal said in a statement.
"Everyone at the club will now be working as hard as we can to ensure Rob is back on the pitch as soon as possible."
Arsenal are fifth in the table with 31 points from 15 matches and host Huddersfield Town in the league on Saturday. (Reporting by Shrivathsa Sridhar in Bengaluru Editing by Toby Davis)
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