The Bavarians took an 18th-minute lead when defender Niklas Sule pounced on a loose ball to score after two botched clearances following a dangerous corner from Joshua Kimmich.
Leverkusen levelled in the 36th with a fortuitous goal, Mueller flummoxing his own goalkeeper Sven Ulreich and turning a free kick from Kerem Demirbay into his own net.
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.
Bayern are still well in charge of the German 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 points.