Tierney suffered an injury in the Premier League game against Liverpool at the Emirates Stadium at the weekend.
The Scotland international left-back was replaced before the half-time interval in North London due to a ligament injury in his left knee.
The 23-year-old former Celtic star will not require surgery and could be back in full training by the middle of next month, but Arsenal manager Arteta has said that he does not know if the youngster will play again this season.
Arteta told Arsenal’s official website: “I don’t know, we’re going to have to go day by day to see how Kieran is feeling, how he is reacting. When we get close to playing time and training with the team, depending where we are and how he’s feeling, we’ll make a decision.”
Tierney has made 23 appearances in the Premier League for Arsenal so far this season, scoring one goal and providing two assists in the process.
The left-back has also made three starts and five substitute appearances in the Europa League for the Gunners this campaign, scoring one goal in the process.