Hitzlsperger faces fitness race for opener
Hitzlsperger, who joined the Premier League club after a poor season split between VfB Stuttgart and Lazio cost him a place in Germany's World Cup squad, was taken off in the 66th minute because of the left thigh problem.
He had earlier set up Mario Gomez for Germany's first goal.
"I hope it is not that bad because I really want to play at the start of the season," he told reporters.
West Ham open the new campaign against the 28-year-old's former club Aston Villa on Saturday.