Bayern are still well in charge of the title race with 59 points after 25 matches although the result will give a glimmer of hope to chasing Borussia Dortmund, who are second on 50 points but have a game in hand. Leverkusen stayed third on 45.
Leverkusen, who had won five of their previous six league matches heading into the game and boasted the second best league form in 2022, levelled in the 36th with a fortuitous goal.
Mueller, who had missed last week's 1-0 win at Eintracht Frankfurt due to a positive COVID-19 test, flummoxed his own goalkeeper Sven Ulreich as he turned a free kick from Kerem Demirbay into his own net.
Bayern substitute Marcel Sabitzer, who replaced Mueller jut past the hour, spurned a one-on-one with goalkeeper Lukas Hradecky in the second period, while striker Robert Lewandowski also missed a chance to win the game for the Bavarians late on.
It was the first time Bayern had drawn a match in the league since the opening day of the season in August when they were held 1-1 at Borussia Moenchengladbach and was also their first draw in the league at home.
Elsewhere on Saturday, an intriguing scrap to take control of the race for a Champions League place ended with honours even as RB Leipzig in fourth were held 1-1 at home by fifth-placed Freiburg, leaving both sides locked on 41 points.
Wolfsburg continued their march away from danger with a 1-0 win at home to seventh-placed Union Berlin, recording a third win in five games to reach 31 points in 12th place.