Bayern Munich's 11th successive victory secured its 23rd national title.
Bastian Schweinsteiger scored the only goal of the game at Eintracht Frankfurt in the 52nd minute, enabling the visitors to win 1-0 and set the record for the earliest Bundesliga title in history.
Bayern clinched the crown after 28 of 34 rounds -- two rounds quicker than its own record of winning in the 30th round in the 1972-73 and 2002-03 seasons.
Munich has 75 points -- 20 more than Borussia Dortmund -- with six rounds of matches remaining.
Club president Uli Hoeness said he couldn't remember a more dominant Bayern Munich side.
"We have played a magnificent season," Hoeness told LIGA total! television. "Rarely have a team won the title in such dominant fashion. In all of the years I have been at Bayern, I cannot remember us being so superior or such clear champions with six games to go."
Bayern can now turn its attention to the treble, being well-placed in their Champions League quarterfinal with Juventus and in the last four of the DFB-Pokal.
"We've got the title now, but things move on," said Robben. "We have got to keep our cool because we still have some important games to come. We want even more from this season and since we are still in two competitions, we want to win them both."
The visitors nearly took the lead after 10 minutes but Xherdan Shaqiri's shot from 14 yards struck the base of the right post.
The decisive breakthrough came in the 52nd minute. Philipp Lahm crossed into the box to Schweinsteiger, who backheeled in a classy goal.
Bayern was looking to double its advantage in the 67th minute but Shaqiri's shot went just wide from 20 yards out.
Frankfurt showed why it is fighting for a spot in international action next season as Bayern goalkeeper Manuel Neuer made a superb save from Srdjan Lakic's point-blank attempt from eight yards out in the 79th minute.
Schweinsteiger was forced to clear off the line three minutes later and the ensuing corner landed at the feet of Takashi Inui, whose powerful shot from 14 yards found the side-netting.
As the visitors celebrated, Frankfurt was left to ponder a run of just one victory in seven matches, remaining on 42 points.
Elsewhere, Dortmund strengthened its position in second, moving six points clear of second-placed Bayer Leverkusen thanks to a 4-2 win at home to struggling Augsburg.
The hosts took the lead through Julian Schieber after 22 minutes, but trailed at the break as Augsburg hit back through Daniel Baier and Kevin Vogt. Schieber got his second to level in the 52nd minute before goals from Neven Subotic and Robert Lewandowski sealed the win for Dortmund.
Defeat left Augsburg just a point above second-bottom Hoffenheim.
Leverkusen was held 1-1 by Wolfsburg, allowing Schalke to close the gap on the final automatic Champions League place to four points with a 2-0 win at Werder Bremen.
At the other end of the table, basement boys Greuther Furth slipped a step closer to an immediate return to the second tier as it went down 1-0 at Borussia Monchengladbach.
There was no response from Hamburg to their humiliation by Bayern as they went down 1-0 at home to Freiburg. Jonathan Schmid had the only goal of the game in the 69th minute.
Information from Press Association was used in this report.