The Belgian, who had been nursing a virus in recent days, was coaching the team before feeling unwell and being rushed to hospital.
"Vincent Kompany had to seek medical treatment on Friday after collapsing during training for FC Bayern's amateurs. The first-team coach had been watching the second team's session," Bayern said in a statement.
"Kompany will undergo thorough examination in the hospital and remain in medical care. For the time being, his coaching staff will manage training and match operations."
"Vincent Kompany’s health is our top priority", Sporting Director Max Eberl said.
"We at FC Bayern will do everything we can to ensure he makes a speedy recovery. Vinnie is receiving all the necessary medical care and support, and all the time he needs. His coaching team, in whom we have complete confidence, will take over his duties. All of us at FC Bayern wish Vinnie a speedy recovery."
The Bundesliga leaders, who drew 2-2 at home against Arsenal in the Champions League earlier this week, are due to travel to Freiburg on Sunday.