Ex-Chelsea player Werner, 26, was taken off in the first half of Leipzig's 4-0 Champions League group-stage win against Shakhtar Donetsk on Wednesday.
“Scans today in Leipzig showed that he has unfortunately torn the syndesmosis ligament in his left ankle and will therefore be out for the rest of 2022," the Bundesliga team said in a statement.
“A decision on his treatment will be made in the coming days.”
Werner, who has 24 goals in 55 appearances for the national team, was part of the Germany squad at the 2018 World Cup and Euro 2020.
The striker is only the latest player to suffer an injury on the eve of the tournament with England currently sweating over Ben Chilwell, Kyler Walker and Reece James.
Additional reporting by Reuters.