The left-back suffered a knee injury against Liverpool earlier this month.
It was expected that Tierney would miss the rest of the season, and possibly the start of Scotland's Euro2020 campaign.
However, the Gunners have provided a a positive update on Tierney on their website.
The update reads: "Kieran sustained ligament damage to his left knee during the match against Liverpool on April 3.
"Kieran continues to make positive progress and is hoping to be back in training within two to three weeks."