The 23-year-old has been one of the Gunners' standout performers in what has been a disappointing campaign overall.
However, Tierney sustained an injury in the recent 3-0 loss to Liverpool, which a scan confirmed was ligament damage.
Having initially been ruled out for at least a month, Arteta has now provided a worrying update over the defender's fitness.
"Kieran is out, probably for the season," he said. "We are going to need different options in that position."
Tierney could now be doubtful for Scotland's Euro 2020 campaign, which begins with a group game against Czech Republic on June 14. body check tags ::