Bosnia-Herzegovina left-back Kolasinac, 27, began his career with the German side before moving to Arsenal in 2017.
"We cannot sustain the numbers we have in certain positions," Arteta had said earlier on Thursday.
"There are some players that are going to go on loan and going to leave."
He added: "That is the priority. Then we will see if we have the right opportunity in the positions where we need some more help."
Kolasanic has made 113 appearances for Arsenal and was part of last season's FA Cup-winning squad.
This term, he has started only one Premier League match but has featured in the Europa League and Carabao Cup.
Arsenal technical director Edu said: "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."