The midfielder suffered the blow while playing for the Germany Under-21s this week, while Joe Allen could also be a casualty.
The 24-year-old injured his knee during Wales's 2-1 victory over Andorra in their opening Euro 2016 qualifier.
"We've got Emre Can back from Germany, who could be out for up to six weeks because of his ankle," Rodgers said in this afternoon's press conference.
"We've got Joe Allen back from playing on awful pitch and he has an issue with his knee. We just need to assess that for the weekend. Those are the types of things than can happen in games and it's unfortunate."