The England captain was sidelined for his country's recent international friendly against Brazil, a match the Three Lions lost 1-0.
He also missed the subsequent 2-2 draw with Belgium due to an ankle injury sustained while on club duty.
Initially, the issue was not deemed serious, but with the striker yet to recover from his injury, he could miss their important game against Madrid.
Kane’s fitness a worry for Bayern
Bayern manager Vincent Kompany had described it as a precautionary measure after Kane twisted his ankle in a Bundesliga match.
However, despite the initial optimism, Kane was unable to participate in either of England's fixtures during the international break, raising concerns at his club.
The striker's absence is a significant blow, and his recovery is being closely monitored ahead of a crucial period for the German champions.
Bayern Munich is scheduled to face Freiburg in a pivotal Bundesliga clash this Saturday as they edge closer to the title.
Following that, they will travel to Spain to take on Real Madrid for the first leg of their Champions League quarter-final tie.
Since his transfer from Tottenham Hotspur in the summer of 2023, Kane has been in sensational form for Bayern.
The prolific forward has scored an impressive 37 goals in just 35 appearances across all competitions this season.