"Vinnie" will get all the time he needs. We will not set any time frames now, sports director Max Eberl said at a press conference.
Kompany was taken to hospital late on Friday afternoon after the 40-year-old collapsed at the club's training ground. He has been suffering from a viral infection for some time.
"First of all, we need to find out what it is, and then we can calmly discuss the recovery time. We are talking about weeks, not days. We all need to be aware of that," Eberl said.
Assistant coach Aaron Danks will lead the team away against Freiburg in the Bundesliga on Sunday.