The result could spell a premature end to their title hopes after 18 games although second-placed Mainz 05 and Bayer Leverkusen, also on 33 points in third spot, plunged to defeat.
"We are all very disappointed," said Bayern coach Louis van Gaal. "It should have been 3-0 at half-time for us but instead we made mistakes.
"You can't win if you make mistakes like that."
Bayern took a seventh-minute lead when Wolfsburg keeper Diego Benaglio raced out of the box and his attempted clearance hit Thomas Muller's leg before rolling into the net.
Both sides missed first-half penalties and Bayern playmaker Ribery limped off with a knee injury in the 17th minute, fit-again Arjen Robben coming on for his first appearance of the season.
Sascha Riether then gave troubled Wolfsburg coach Steve McClaren something to smile about with his 86th-minute equaliser.
Bayern are fifth on 30 points, way behind leaders Borussia Dortmund on 46.
Dortmund stretched their lead to 13 points with a 3-1 triumph at Leverkusen on Friday and a day later Mainz failed to make inroads on their deficit, slumping to a 1-0 defeat at VfB Stuttgart, Martin Harnik on target with 11 minutes to go.
HAMBURG WIN
A sixth league goal of the season by Ruud van Nistelrooy, who is on Real Madrid coach Jose Mourinho's transfer wish-list, gave Hamburg SV a 1-0 victory at Schalke 04 that lifted them to seventh with 27 points.
Werder Bremen climbed to 12th after returning to winning ways by beating Hoffenheim 2-1 with a last-gasp goal from Torsten Frings.
Bottom club Borussia Moenchengladbach grabbed a 1-0 win at Nuremberg to close the gap to two points on second from bottom Cologne.
It was supposed to be the start of Bayern's renewed battle for the championship, following the winter break, and the aggressive visitors were on course early on when Mario Gomez rattled the crossbar and then Mueller gave them the lead.
Philipp Lahm, however, hit the post with a 21st-minute penalty.
Wolfsburg fought back to win a penalty in the dying seconds of the first half but Bayern's new first choice keeper Thomas Kraft did well to palm Grafite's spot-kick on to the bar.
Robben's arrival added pace for Bayern who dominated the second half without converting any of their half-dozen chances and the Bavarians were punished when Riether levelled.
