Germany coach Julian Nagelsmann admitted on Thursday that Fullkrug had suffered the injury while training with West Ham.
The 32-year-old broke down with a serious thigh tear and faces several weeks on the sidelines.
Nagelsmann had planned to bring in Fullkrug as an injury replacement for Stuttgart striker Jamie Leweling, who missed the game against Luxembourg with adductor problems.
But he received news from West Ham of Fullkrug's setback before the tie on Friday night.