Wirtz injured his ankle in Monday's 1-0 win over the Netherlands in Munich and did not return to the pitch after half-time.
In a statement issued Tuesday, Leverkusen said an MRI confirmed Wirtz "suffered a capsule injury to his right ankle at the end of the first half", adding it was "still unclear when he will return to training".
The 21-year-old "is currently undergoing treatment in Leverkusen", the club indicated. Germany coach Julian Nagelsmann said after Monday's match: "Flo has a bit of a problem with a tendon... we hope it's nothing bad."
Wirtz was named Bundesliga player of the season last year as Leverkusen claimed an undefeated league and cup double. He has started this season in fine form, scoring six goals and laying on one assist for Leverkusen.