Bayern didn't take long to grab the lead, as Ribery's 25-yard drive after seven minutes proved too hot for City stopper Joe Hart to handle.
A further two goals in the second half from Thomas Muller and Arjen Robben dealt City's European ambitions a harsh reality check, although Alvaro Negredo's wonderful consolation and a late dismissal for Jerome Boateng had Bayern panicking briefly.
Bayern signalled their intentions early on, with David Alaba and Ribery enjoying space down the left, while Rafinha and Robben stretched the home defence even more down the right.
Robben flashed an early header just wide from an Alaba cross, and not long afterwards Ribery exploited the space by unleashing a low drive, though Hart will perhaps be disappointed he couldn't keep it out.
City toiled in their attempts to fashion a chance as Bayern's relentless closing down left them beleaguered. A quick Yaya Toure free-kick did find Sergio Aguero after 33 minutes, but the striker's finish was well wide.
Bayern continued to dominate the second half after a brief spell of City on top. After 56 minutes a long ball from Dante allowed Muller to pounce through after Gael Clichy inexplicably stopped watching his man, and the German forward was able to evade Hart to slot into an empty net.
Just four minutes later the footballing lesson was complete. Bayern's pressing game paid dividends as the ball was won in midfield by Phillip Lahm, whose quick pass gave Robben the space to run into, with his right-footed shot beating Hart at his near post.
In truth, Bayern could have extended their lead comfortably, with their excellent passing game leaving City bewildered as Robben, Kroos and Muller - who smashed the crossbar - missing opportunities.
James Milner's late curled strike was well saved by Manuel Neuer, but substitute Alvaro Negredo went one better with a wonderful curling effort on 80 minutes to give City hope.
Their hope for a dramatic comeback was multiplied after 86 minutes when Yaya Toure raced through, only to be brought down cynically by Boateng. The defender received a straight red card and David Silva crashed the resulting free-kick off the crossbar as City's late rally was unrewarded.
The overwhelming feeling was that a City side that thrashed Manchester United just 10 days previously were taught a footballing lesson.
Manuel Pellegrini was appointed by City in the summer in expectation he could improve the club's standing in Europe but this was clear indication of the scale of the task ahead.
Yet as brilliant as the Germans were, the defence and Hart had a harrowing time.
Hart was at fault for Bayern's opener and was beaten too easily for the third goal, while Gael Clichy was the chief culprit for the second.