Bayern, double winners for the past two seasons, had enough chances to beat their Bavarian rivals comfortably but Roy Makaay missed an open goal in the second half and Lukas Podolski made little impact after coming on as a substitute.
A draw was enough for Nuremberg to edge back to the top with seven points from their three matches played.
Bayern are behind them on goal difference, sharing second spot with Schalke 04 after their 2-0 win over Werder Bremen on Friday.
Hertha Berlin and Mainz will have chances to join the clubs on seven points when they play on Sunday. Hertha are away at Hamburg SV, while Mainz host Eintracht Frankfurt in a local derby.
Bayern coach Felix Magath once again left out Owen Hargreaves, the England midfielder who is eager for a move to Manchester United.
Without Hargreaves, the champions showed little threat through the middle but Bastian Schweinsteiger, the 21-year-old Germany winger, did at least look a consistent threat on the left.
Schweinsteiger went close with a powerful long-range shot in the 16th minute.
Bayern should have scored in the 27th minute when Hasan Salihamidzic wriggled through a couple of challenges and into the box only to shoot straight at the keeper.
Nuremberg briefly threatened towards the end of the first half, with Markus Schroth clattering a shot wide in the best of their few chances.
The second half was all Bayern and was summed up by Makaay's embarrassing miss four minutes after the restart.
The Dutch striker showed excellent control to take Schweinsteiger's low pass and take the ball round the keeper. Inexplicably, he then put a shot wide from a few metres out.
"Sadly you get days like this, when you have chances but the ball just won't go in," Magath said. "We don't have maximum points but we do have seven from three games and we can live with that."
