The club made the announcement while reporting the latest news on some of their injured players, ahead of their Europa League clash against Standard Liege on Thursday.
“Dislocated right shoulder during the West Ham United match. Currently undergoing further assessment and investigations,” Arsenal stated on their website.
The injury means Tierney is a huge doubt for the home game against Manchester City.
Arsenal’s other full-back Hector Bellerin was injured during the warm-up at London Stadium and will miss the Gunners’ Europa League clash with Standard Liege.
Bellerin will then be assessed ahead of the Manchester City match on Sunday.
Also missing for Arsenal’s trip to Belgium on Thursday is Granit Xhaka, who suffered a concussion against West Ham.
The Switzerland international will also miss the Premier League clash with the Citizens.
Nicolas Pepe has also been ruled out of the Europa League tie after the forward bruised his knee against West Ham. He is expected to return for the City match.
Pepe was Arsenal’s hero in their comeback victory over West Ham on Monday.
The summer signing produced and assist and netted a goal as Arsenal won their first match in 10.
Arsenal returned to winning ways on Monday after going nine consecutive games without a victory.
They are now in the ninth position on 22 points, seven points away from the fourth position.
They lead their Europa League Group F standings on 10 points, just one point ahead of Eintracht Frankfurt who are second.
In the third position is Arsenal’s opponent on Thursday Standard Liege who are on seven points while Vitoria de Guimaraes are bottom on just two points.
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