The 23-year-old, who has scored three goals this summer, limped out of his side's 3-1 win over Japan in the semi-finals on Tuesday.
Tena told reporters: "Unfortunately, he has a muscle injury. [We] don't know the magnitude of the injury yet, we have to wait and run some tests. He's doubtful at this point. We have to find out."
The final of the men's competition takes place on Saturday at Wembley Stadium.