Bayern Munich head coach Vincent Kompany has been discharged from hospital and is "doing well" following his collapse at the club's training ground.

Kompany, 40, was rushed to hospital last Friday after taking ill as he watched the club's second team train.

The cause has been identified as meningeal irritation - an inflammation of the protective membrane surrounding the brain and spinal cord.

"Given the circumstances, he's doing well," Max Eberl, the club's board member for sports, told German broadcaster ARD on Wednesday.

"He was discharged from the hospital today. That is the biggest and best news for all of us."

No timeline has been set for Kompany's return and Bayern said on Saturday that it would be a matter of "weeks, not days" until the former Manchester City defender returned to the dugout.

English assistant coach Aaron Danks has taken over in Kompany's absence and oversaw a 3-1 win at Freiburg on Sunday.

Kompany had been nursing a virus in the days before his collapse and missed some team training sessions.

The Belgian missed a pre-match news conference prior to Bayern's Champions League game against Arsenal last Tuesday, but was subsequently on the touchline for the match on Wednesday.

"It's a meningeal irritation that caused this incident on Friday. He will now rest and take medication," said Eberl, speaking before Bayern's German Cup tie against Magdeburg.

"I am very confident that he will be back on the touchline, operating at 100% very soon."

Current leaders Bayern face title rivals Borussia Dortmund in the Bundesliga on Saturday.