The Japan international has been struggling with the issue since the turn of the year but was fit enough to play against Liverpool in the EFL Cup in midweek.
However, Tomiyasu's injury flared up again before the 0-0 draw with Burnley on Sunday, which also forced him to pull out of international duty for the upcoming break.
Arteta has now confirmed that the right-back's issue will not be a quick fix, telling reporters: "Well, Tomiyasu had an injury and we didn't have anybody to play in that position against Liverpool, as quoted by arsenal.com.
"He really wanted to push, he tried and he played the 90 minutes, and he felt it again. He will be out for a few weeks."
Tomiyasu has already won favour with the Emirates faithful since his arrival from Bologna, recording one assist from 16 Premier League starts in an Arsenal shirt this term. body check tags ::