Officials and coaches rally behind Rangnick
The 53-year-old's unexpected announcement jolted Germany's football world, still sensitive to mental and physical health issues following the 2009 suicide of Germany goalkeeper Robert Enke.
Enke, who was on track to become Germany's first choice for the 2010 World Cup, had been suffering from depression but kept it secret for years for fear of professional repercussions.
He threw himself in front of a speeding train in November 2009.
After four years at Hoffenheim, taking them from the third division to the Bundesliga and then the top of the standings at the halfway mark in 2008, Rangnick left last January and took over at Schalke 04 in March.
"His energy levels are finished," Thorsten Rarreck, Schalke team doctor, told reporters. "A Bayern Munich coach once said: 'Empty bottle, and that is what it is.'
"When he took over here after his Hoffenheim period there was no recovery time for him. He has reached his physical limits but it is a reversible situation. This is a preventive measure."
Rangnick himself said in a brief statement he could not fulfill the club's ambitions in his current state and needed a break after a successful six-month stint in which he led them to the Champions League semi-finals and German Cup victory.
"I have great respect for his decision and the fact that he openly deals with his condition," said German football association (DFB) boss Theo Zwanziger.
"Maybe the situation in this tough business called professional football has changed following the tragic death of Robert Enke.
"Maybe weaknesses and illnesses are tolerated and respected more than they were two years ago. At least that is what I hope."
Germany coach Joachim Low called it a "show of strength, to publicly admit that the batteries are empty."
His departure from top flight football after admitting to burnout also got the support of his Schalke predecessor Felix Magath.
"This is a personal, courageous and respectful move," Magath said. "I know from personal experience how demanding and burdensome the coaching job can be."
Bayer Leverkusen coach Robin Dutt added: "We all think that football is the most important thing in the world and now we realise that it is not the most important thing.
"We all need to have more respect for each other because in this system everyone puts pressure on everyone.
"Players on coaches, coaches on players, media on players and coaches and fans on players and coaches."