Lahm collapsed during a morning session at the club's training ground and needed help to be taken from the field, before heading to hospital.
The exact injury suffered by the 31-year-old remains unclear, but Bayern revealed their fears he could be set for an extended period on the sidelines.
"Bayern remains hampered by injury problems," a club statement began.
"During the public workout on Tuesday, captain Phlipp Lahm had to abort the session.
"The 31-year-old went to ground holding his right foot under no opponent's challenge and had to be taken from the training pitch on a golf cart."
Lahm has played 18 matches in all competitions for Bayern this season, scoring two goals.
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