Kirchhoff joined the club on a temporary basis from Bayern Munich this winter after struggling to force his way into Pep Guardiola's side, admitting he was relieved to be given the chance to secure regular first-team football.
However, the versatile defender was injured at Schalke's training camp in Qatar and is due to fly back to Germany on Tuesday.
General manager Horst Heldt stated via the club's official Twitter acount: "A ligament is damaged.
"It makes more sense that he travels back to Germany on Tuesday."
Schalke were involved in friendly action on Monday, with a double from Adam Szalai securing a 2-1 win over Al-Gharafa.