Xavi's side drop into the Europa League and will not appear in the knockout stages of Europe's premier club competition for the first time since the 2003-2004 season.
Already assured of top spot in Group E, first-half goals from Thomas Muller and Leroy Sane put Bayern well on the way to progressing with a 100 per cent record.
Jamal Musiala ensured that Julian Nagelsmann's side did just that when he sealed the victory just after the hour mark in another routine victory for the hosts in this fixture.
To avoid elimination, Barca needed to win or hope that Benfica failed to beat Dynamo Kiev elsewhere in the final round of group fixtures.
Jordi Alba tested Manuel Neuer from distance, while Ousmane Dembele swept a shot over from Memphis Depay's square ball.
But Barca fell behind in the 34th minute; Robert Lewandowski cleverly twisting and turning before crossing for Muller, whose looping header crossed the line before Ronald Araujo could volley clear.
Bayern doubled its lead just before the break with Sane's powerful 30-yard strike completely perplexing Marc-Andre ter Stegen.
Sane squandered a golden opportunity for his second goal shortly after the restart when somehow failing to turn the ball home from inside the six-yard box after Kingsley Coman cushioned Alphonso Davies' cross into his path.
Bayern's third goal did arrive in the 62nd minute as Musiala sealed the deal by slotting home following a strong run and cross by Davies.