The 31-year-old had previously been forced off before the end of last weekend's 1-1 draw with champions Bayer Leverkusen, although that was a knock from a heavy tackle rather than anything truly sinister.
Kane was fine to play the full 90 in Bayern's midweek Champions League loss to Aston Villa and led the line in Sunday's top-of-the-table clash with Frankfurt, providing an assist for Michael Olise.
However, the former Tottenham Hotspur striker then went down with a leg problem midway through the second half, and he was replaced by Mathys Tel for the remainder of that six-goal thriller.
While Kompany was optimistic about Kane's chances of a swift recovery last weekend, the Bayern boss - who also lost Dayot Upamecano to injury on Sunday - was not so confident this time around.
Kompany unsure if Kane's injury is serious
"It's still too early to say what Kane has. We hope it's nothing serious. Same goes for (Dayot) Upamecano. This week was a real test for our team to see how dominant we can be against these teams three times a week," Kompany told the media.
Kane is due to head to St George's Park this week to link up with the England squad, although it remains to be seen if he will undergo more tests in Germany or be assessed by England's medical staff.
Either way, the striker's latest scare is far from ideal for interim manager Carsley, who also saw Aston Villa's Ezri Konsa and Nottingham Forest's Morgan Gibbs-White sustain issues at the weekend.
Konsa was brought off in the first half of the Lions' 0-0 draw with Manchester United, and Unai Emery admitted after the game that the defender appeared to hurt his hamstring, which would likely rule him out of the international period.
Meanwhile, Gibbs-White appeared to get his foot awkwardly caught in the turf during Forest's 1-1 stalemate with Chelsea, but Nuno Espirito Santo could not say how severe his problem was.
Who could replace Kane in England matches?
As Al-Ahli's Ivan Toney has missed out on selection for the second international window running, one of two like-for-like options to replace Kane at the tip of the England attack is Villa star Ollie Watkins.
The 28-year-old has only ever started five competitive games for England, appearing in another 10 games off the bench, including the Three Lions' dramatic Euro 2024 semi-final success over the Netherlands where he netted a late winner.
However, the skipper's injury could also offer Tottenham Hotspur talisman Dominic Solanke the opportunity to make his first-ever England start, seven years after his maiden appearance in November 2017.
The ex-Bournemouth man had not been called up to another squad since a late cameo in that friendly against Brazil, but he rejoins the squad in strong form domestically, either scoring or assisting in his last three Premier League appearances.
England face Greece in their first Nations League game of the month on October 10, three days before travelling to Finland in their fourth League B Group 2 encounter.