The Manchester City midfielder has started both games for Joachim Low's side in the tournament so far, but he was one of four players to sit out of training at the beginning of this week - along with Mats Hummels, Thomas Muller and Lukas Klostermann.
Manchester Evening News reports that Gundogan is suffering with a calf injury and faces a race against time to be fit enough to start in Munich on Wednesday.
The 30-year-old only missed one game for Pep Guardiola's side during the 2020-21 campaign through injury, after initially missing five games between September and October due to coronavirus.
Germany can win the group on Wednesday with a win against Hungary but will need to rely on France dropping points against Portugal. body check tags ::