The victory opened a 10-point gap between Bayern and second-placed Borussia Dortmund who, despite having three games in hand, cannot catch the champions.
A first-half goal by Robert Lewandowski saw the German powerhouse become the first club in a major European league to win the title after returning to play amid the coronavirus pandemic. Bayern are still in pursuit of a Treble, as they will play for the German Cup and remain alive in the Champions League.
Amid a rainy backdrop at Bremen's Weserstadion, the Bavarians gradually gained ground and broke the deadlock with defender Jerome Boateng's superb pass for Lewandowski, who turned in the box and grabbed his 31st goal of the campaign just before halftime.
The Polish forward, who scored for Bayern on his return from a one-match suspension, is chasing the 40-goal record for one season set by Gerd Mueller in 1972 and had a string of good chances after the break to add to his tally.
But it was keeper Manuel Neuer who proved key for Bayern after they were left with 10 men for the final 10 minutes following the dismissal of Alphonso Davies, making a sensational one-handed save to ensure yet another league title.
With fans still barred from games, the players celebrated their title in the empty stadium.
A German ban on mass gatherings mean that the club does not know when it will be able to celebrate the win with its supporters. It has yet to be announced when DFL CEO Christian Seifert will present the champions with the Meisterschale, the trophy for the Bundesliga title.
Bayern Munich won their past 11 Bundesliga games and picked up 52 of a possible 54 points since losing 2-1 at Borussia Monchengladbach in early December. Only RB Leipzig were able to take points off them with a goalless draw at the Allianz Arena in early February.
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Bayern had dropped to seventh in the standings, seven points behind then-leaders Gladbach, following their last defeat. But after back-to-back losses against Leverkusen and Gladbach, coach Hansi Flick turned the club's season around.
"It is sensational the kind of football we have played in the past few months," Flick said after Tuesday's win. "You could feel the passion the joy for the game and the team spirit."
"We have now taken the first step and reached our big goal," he added after the team celebrated their triumph in front of empty stands due to the pandemic.
"But we also have the Cup in our sights and then obviously the Champions League games are something you cannot plan for and we still need to survive the Chelsea game."
Flick, a former assistant of Germany manager Joachim Low, took over from Niko Kovac, who had been sacked following a 5-1 defeat at Eintracht Frankfurt in early November. In his first Bundesliga game in charge, Flick led his new team to a 4-0 win over Borussia Dortmund.
"It's a strange, curious championship. In autumn, we were seven points behind. We were weaker, and you have to say the opposition failed to capitalise. Hansi Flick took over and has done a great job," Bayern CEO Karl-Heinz Rummenigge said.
Bayern Munich's star players this season include Lewandowski and former Germany international Thomas Muller as well as Austrian defender David Alaba. Canadian left-back Davies, meanwhile, has been Bundesliga's most-improved player.
At just 19, Davies is set to become a cornerstone of the new Bayern Munich generation alongside the likes of Germany internationals Joshua Kimmich, Leon Goretzka, Serge Gnabry and centre-back Niklas Sule, who missed vast parts of the season with an ACL tear.
Bayern Munich have averaged 84.57 points per season over their past seven Bundesliga titles. The only other club to reach more than 80 points in one season was Borussia Dortmund's last title-winning side in the 2011-12 season.
The club have dominated the Bundesliga in the past seven years with the average gap between first and second place over 14 points. Borussia Dortmund have finished second four times while RB Leipzig, VfL Wolfsburg and Schalke 04 have each filled the runners-up spot once in that time.
Borussia Dortmund are likely to finish second this term and could reach a maximum of 75 points. The club dropped crucial points in the first half of the season when they only won 30 of a maximum of 51 points.
Information from Reuters was used in this report.