A first-versus-second clash heading into the weekend, the reigning champions came into the game having won their previous four league fixtures, scoring 16 goals and conceding none in the process.
But Bayern's fluidity was missing for large swathes of the match at Borussia-Park as they were shut out for the second time this season.
Gladbach carried most of the game's true attacking threat, with well-timed counter-attacks routinely piercing Pep Guardiola's newly favoured 3-4-3 system.
Max Kruse and Andre Hahn both had good sights of goal after rapid breakaways, but Germany number one Manuel Neuer proved typically tough to beat.
For all of Bayern's dominance of the ball in advanced areas, Martin Stranzl and Alvaro Dominguez were rock-solid in the heart of the home defence to preserve a draw that means both teams remain unbeaten in the Bundesliga this term.
The draw maintains Bayern's four-point advantage over Lucien Favre's side, but may give Gladbach confidence to keep the pressure on Guardiola's men in the seeming absence of a challenge from Borussia Dortmund this term.
Gladbach may have been nervous having seen Bayern travel to Roma and put seven past the Italians in the UEFA Champions League in midweek - but they stood much firmer.
Yann Sommer had to be alert to tip David Alaba's goalbound cross onto the post 10 minutes in, but Bayern's front three of Robert Lewandowski, Mario Gotze and Thomas Muller often found themselves getting in each other's way.
The hosts retained a threat on the break and Kruse was released clear on Neuer but the Germany number one stood firm, before a Lewandowski effort was deflected agonisingly wide of the left-hand post to keep scores level just before the interval.
More good work on the break from Gladbach put Hahn in the clear 10 minutes after the interval, but Neuer denied the winger to his right and Mehdi Benatia slid in to prevent Raffael tapping into the unguarded net.
Juan Bernat hit the side netting after creative play from Philipp Lahm and Sommer denied Gotze at full stretch as Bayern pressed on with Franck Ribery introduced to add to their options.
Gotze saw a late penalty appeal waved away as Stranzl lunged in and Bayern were ultimately unable to break down a dogged Gladbach side.
Though far from damaging, a rare toothless display will worry Guardiola with Dortmund set to visit the Allianz Arena next week desperate to kickstart their domestic campaign.
