The flamboyant Dutchman had been due to leave at the end of the season but Bayern brought forward his farewell by five games after they dropped out of the Champions League qualifying-round spot.
"Bayern have given coach Louis Van Gaal leave of absence with immediate effect," the club said on their website on Sunday.
Jupp Heynckes, currently at second-placed Bayer Leverkusen, has already been named as Bayern's coach for next season, his third stint at the club, and Andries Jonker would be interim coach for the rest of this term, Bayern said.
Hanover 96 replaced Bayern in third place, the Champions League qualifying-round spot, after beating Mainz 05 2-0 on Saturday.
Bayern have dropped to fourth, which would mean a place in next season's Europa League, a huge indignity for Germany's biggest club.
With next season's Champions League final to be staged in Munich at their own Allianz Arena, it would be a catastrophe for Bayern if they missed out on Europe's top club competition.
"This was not a spur-of-the-moment decision, the dissatisfaction has been growing amongst us for weeks," Bayern CEO Karl-Heinz Rummenigge told a news conference.
"We must do everything we can to finish third. We must make the best decision for Bayern, which is what we have done.
Club president Uli Hoeness criticised Van Gaal's decision to replace experienced goalkeeper Joerg Butt with 22-year-old Thomas Kraft.
"Van Gaal did not take our advice. It has caused great unease in the whole defence," he said.
KEY INJURIES
Bayern, who have suffered injuries to key forwards Franck Ribery and Arjen Robben this season, have 52 points from 29 games, including 15 wins and seven draws.
Sunday's announcement was a far cry from the huge street parties less than a year ago after Van Gaal won the Bundesliga and German Cup and led Bayern to the Champions League final in his first season in charge.
In September, Bayern extended Van Gaal's contract by one year to the end of the 2011/12 season but reversed that decision in March when Bayern's chances of retaining the Bundesliga evaporated with a 3-1 home defeat by Borussia Dortmund.
Worse was to follow when Bayern were knocked out of the Champions League by Inter Milan - their conquerors in last season's final - in the last 16 after conceding a last-minute goal and losing 3-2 at home in the second leg, having won the first match 1-0 away.
It was not only on the pitch that Van Gaal failed to deliver. He was also involved in a very public war of words earlier this season with Hoeness who called Van Gaal a "one-man show" who never took any advice.
Van Gaal, 59, has also coached Ajax Amsterdam and Barcelona, winning the Champions League with the Dutch side in 1995.
He coached the Netherlands team which failed to qualify for the 2002 World Cup. At Barcelona, he famously fell out with Brazilian Rivaldo and Argentine playmaker Juan Roman Riquelm
