The England captain was forced off late in Bayern's 1-1 draw with champions Bayer Leverkusen after suffering an ankle injury.
The striker went down after being caught by Amine Adli and received treatment before being replaced by Thomas Muller with four minutes remaining.
'I'm not a doctor, but I hope it's nothing serious. It's still early to say. Hopefully he'll be fit for Wednesday,' Kompany told Sky Sports.
Bayern sporting director Max Eberl added: 'If Harry goes off the pitch, then it's something. Now I hope he's made of sturdy English wood.'
Harry Kane is an injury doubt for Bayern Munich's Champions League clash with Aston Villa
Kane will undergo an examination on Sunday ahead of Bayern's trip to Villa Park, with the side hopeful of making it two wins from two in the Champions League this season.
The former Tottenham striker has started the season brightly with 10 goals in. seven games across all competitions.
England interim manager will also be be hopeful Kane's injury is not serious, with the Three Lions set to face Greece and Finland in the Nations League in the coming weeks.
The draw at the Allianz Arena brought an end to Bayern's perfect start of the season having won all their previous six matches.
Bayer Leverkusen took the lead when Robert Andrich struck the ball into the bottom corner from the edge of the box after being teed up by Granit Xhaka inside 31 minutes.
The hosts got on level terms eight minutes later through Aleksandar Pavlovic's superb strike from 25 yards into the top corner.