The Bosnia defender, 27, will head back to the club where he joined the youth set-up and went on to become a first-team regular before moving to the Premier League in June 2017.
Arsenal technical director Edu told the club website: “Sead needs to be playing regularly, so we have decided together that a move back to Germany with Schalke will benefit him at this moment.
Schalke are currently bottom of the Bundesliga with just four points and without a win all season.