The 26-year-old was absent from the German national team's training session on Tuesday morning, and journalists on the ground were told he is struggling with his knee.
The former Manchester City player also missed five of Bayern Munich's games in late October when a muscle injury sidelined him for 16 days.
With Sane out of contention, the door has been opened for the likes of veteran Germany international Thomas Muller to step in, but he has also been hampered by a few niggles in recent weeks and may not be ready.
National team head coach Hansi Flick may have to tinker with his attacking options now, with Serge Gnabry, Jonas Hofmann, and Julian Brandt the most likely replacements.
Germany will get their 2022 World Cup underway against Japan in a Group E encounter at the Khalifa International Stadium on Wednesday.