Fay, 35, has found herself on the bench at City this season behind Lee Alexander, and needs game time ahead of the European Championships this summer.
The Scotland captain, who is closing in on 200 appearances for her country, signed for City in January last year.
"It is with deep regret that Gemma Fay has left the club," said head coach Scott Booth.
"She didn't want to leave and we definitely wanted her to stay but ultimately she felt at this point in her career playing every week was incredibly important, especially given the upcoming Euro finals."
Fay spent seven years at Celtic before moving to the Scottish champions, having previously played for Hibernian, Leeds, Brighton, Ayr and Aberdeen.
Scotland goalkeeper Gemma Fay has left Glasgow City to sign for Icelandic side FC Stjarnan.