Gyau collected his second international cap against Ecuador on Friday, but hobbled off with a suspected sprained left knee.
The Borussia Dortmund midfielder initially told reporters the injury was not serious following the 1-1 draw in Connecticut, but Klinsmann revealed the 22-year-old will undergo surgery.
"Its unfortunately not a little minor thing - he is getting surgery back in Germany and he will be out probably until January," Klinsmann said.
"Unfortunately that is the result of an MRI that was taken [in Florida], he flew over to Germany and their team doctors decided to have him undergo surgery so he will be out for quite a while.
"That is a real bummer because he really gave us some spark."
The injury saps the momentum out of Gyau's recent breakthroughs, as the Tampa native debuted for both club Dortmund and country in September.
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