Germany striker Miroslav Klose scored his tenth Bundesliga goal to seal the win at the Veltins Arena in Gelsenkirchen as Schalke fell to their third straight league defeat leaving Bayern top with a four-point lead.
Werder Bremen stay second after their 2-0 win over Borussia Dortmund.
Since his summer switch from Marseille, Ribery has become the Bundesliga's brightest star and was instrumental is his side's first win at Schalke for 10 years. But in his weekly column in German tabloid Bild. Beckenbauer says Bayern rely too much on Ribery, who returned from injury to put his side in the German Cup semi-finals with a winning penalty against 1860 Munich in midweek.
"The cup win shows how much Bayern depend on Ribery and in my opinion, it is too much," wrote Beckenbauer, who is Bayern's president. "Without him, the team is static and shows no imagination. His return from injury gave the team an electric shock. Suddenly, the other players move more and are more motivated."
Ribery ruled the midfield against Schalke and Bayern had several chances to improve the lead through Klose and the Bundesliga's top-scorer Luca Toni, while Schalke offered little apart from a handful of near-misses by German national team striker Kevin Kuranyi.
The future of Royal Blues coach Mirko Slomka now hangs in the balance after three-straight league defeats, but a Champions League win at FC Porto next week would put his side in the quarter-finals.
Werder Bremen remain four points adrift of Bayern with their 2-0 win over Borussia Dortmund thanks to a double-strike from Swedish striker Markus Rosenberg.
In the days other results, Karlsruhe moved into fifth place with a 3-1 win over VfL Wolfsburg. Strugglers Hansa Rostock and Arminia Bielefeld shared a point in their 1-1 draw as they both remain just above the relegation zone.
After their humiliating German Cup quarter-final defeat at the hands of second division relegation candidates Carl Zeiss Jena, defending champions VfB Stuttgart had their game with Energie Cottbus cancelled by bad weather. Nuremberg's misery continues as they remain locked in the bottom three after their 2-1 defeat by Hanover.
On Friday, Hertha Berlin remain in midtable after picking up three points when they beat bottom side Duisburg 2-0 at the Olympic Stadium. And on Sunday, third-placed Bayer Leverkusen are at VfL Bochum while fourth-placed Hamburg take on Eintracht Frankfurt.