The left-footed midfielder sustained the injury during Arsenal's 3-1 win over Tottenham Hotspur in the North London derby.
Xhaka, being accidentally caught by Lucas Moura after the Brazilian suffered a challenge by Thomas Partey was replaced by Albert Sambi Lokonga.
Following an examination by a specialist, the 29-year-old is likely to miss the rest of 2021.
A statement by Arsenal disclosing the update of Xhaka's situation read;
"Further to injuring his right knee during Sunday's match against Tottenham Hotspur, assessments and scans have confirmed that Granit Xhaka suffered a significant injury to his medial knee ligament," an Arsenal statement read.
"A specialist consultation took place in London on Tuesday evening which has determined that Granit does not require surgery.
"Granit's recovery and rehabilitation programme will start immediately and we are aiming for him to be back in action in approximately three months.
"Everyone at the club will now be supporting and working hard with Granit to get him back on the pitch as soon as possible."
"Arsenal added: Granit’s recovery and rehabilitation programme will start immediately and we are aiming for him to be back in action in approximately three months. Everyone at the club will now be supporting and working hard with Granit to get him back on the pitch as soon as possible."
The Switzerland international has made four of Arsenal's six Premier League matches this season, missing two as part of his three-gamesuspension following a red card against Manchester City on August 28.
