The 22-year-old Scotland international suffered the injury in only his third Premier League start for the Gunners against West Ham United on Monday.
Tierney was replaced by Sead Kolasinac in the 29th minute following the injury as Arsenal came from a goal down to win 3-1 thanks to second half strikes by Gabriel Martinelli, Nicolas Pepe and Pierre-Emerick Aubameyang.
He subsequently missed Arsenal’s 2-2 draw with Standard Liege in the Europa League on Thursday but will face an extended spell on the sidelines following the prognosis of his injury.
Arsenal announced on their website on Saturday that Tierney will have surgery next week before beginning a three-month rehabilitation program.
Tierney has been blighted by injuries since moving to the Emirates Stadium from Scottish champions Celtic for £25m in the summer.
He had to wait until late September to make his Arsenal debut in a 5-0 win over Nottingham Forest in the Carabao Cup.
Arsenal, who are still without a substantive manager following the dismissal of Unai Emery, are ninth on the league table and host champions Manchester City at the Emirates Stadium on Sunday.
The timescale for Tierney’s injury means Scotland boss Steve Clarke will be sweating on the fitness of the defender.
Scotland face Israel in the first leg of the Euro 2020 play-offs on March 26 at Hampden Park.
