The 53-year-old Rangnick quit Schalke with immediate effect on his own terms after just six months in charge. He was the second German league coach to part company with his club after Hamburg sacked coach Michael Oenning on Monday.
For Saturday's home Bundesliga game against Freiburg, assistant coaches Josef Eichkorn and Markus Gisdol have stepped in for the interim until a replacement is found.
"After long and careful consideration, I have come to the conclusion that I need a break," said Rangnick on Schalke's web page.
"I found it incredibly hard to make a decision like this, but my current energy levels are not high enough to succeed and in particular to advance the team and the club. I am taking this step for the benefit of the team, who I wish every success for the rest of the season."
Schalke's general manager Horst Heldt said the news had taken the club by surprise, but they respected the decision after Rangnick admitted suffering from disturbed sleep, restlessness and poor appetite, especially in the last two weeks.
"It pulled the ground from under our feet, because the signs were not recognisable," said Heldt.
Schalke's chief executive officer Clemens Tönnies echoed that the news had come 'like a lightning strike' and the Royal Blues did not yet have a successor in mind.
Having come to Schalke just two months after leaving Hoffenheim in January, Rangnick has taken few breaks from football since 2005 and Schalke's team doctor Thorsten Rarreck said the coach had done the right thing.
"He realised enough is enough. He has had a killer job for the last five years, if he had taken a four- or five-month break, perhaps this wouldn't have happened," said Rarreck.
"This is very brave of him. I know lots of people who in the same situation would have thought they have to go on. It will take him a few months to recover, but unlike depression, burnout is reversible."
President of the German Football Federation (DFB) Theo Zwanziger said Rangnick's decision shows things have changed slightly in Germany since the tragic suicide of goalkeeper Robert Enke in November 2009 after suffering from depression.
"Perhaps the situation in the hard world of professional football has changed a little bit after all the discussions surrounding the tragic death of Robert Enke," Zwanziger told daily Bild.
Rangnick took over as Schalke boss on March 17 after the Royal Blues sacked Felix Magath, who is now coach of 2009 champions VfL Wolfsburg.