The Dutchman, who only took up the role in March having previously coached PAOK in Greece, revealed that he wanted to take a break from the game.
"I have decided that I now want to make up for the break that I really wanted to do after PAOK Salonika," he said.
The defeat to Bayern was Stevens' fourth in charge, but his return of 13 points from 10 games was enough to keep them in the top flight.
Board member and former Stuttgart striker Fredi Bobic agreed with the 60-year-old's decision to stand down.
"We felt in our conversations that Huub Stevens has his decision well thought out," he said. "We can also understand Huub Stevens' decision and wish him all the best for the future."
Stuttgart, who finished 15th, five points above the relegation play-off, looked on course for a hard-earned point at the Allianz Arena until Claudio Pizarro's injury-time strike won it for the champions.
No announcement has yet been made on who Stevens' successor will be, but he will be tasked with improving on a sub-standard campaign for Stuttgart, who began the process of rebuilding with the signing of defender Florian Klein from Red Bull Salzburg last week.
