Kane hit the bar in an otherwise quiet 45 minutes against the Scottish side. He later told reporters that he had suffered a calf problem.
"We'll have a scan tonight and then we'll see. I'm not sure if I can play against Frankfurt on Sunday," he told reporters at the Allianz Arena.
Kane also said that a jaw injury he suffered in a collision against Bayer Leverkusen last Saturday was still troubling him.
Bayern Munich's Sporting Director Max Eberl also confirmed that an ankle issue had been affecting the England captain's mobility in the first half against Celtic.
When asked about Kane's injury problems, Vincent Kompany said that he couldn't say at this moment how long Kane will be out for.
However, Kane reassured reporters that he is "OK".
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