The Germans, undefeated under coach Hansi Flick with eight wins and four draws, needed a ninth minute equaliser through Jonas Hofmann to earn a point.
Flick's team is in third place in the standings with three points. Hungary have four and Italy are top on five.
Looking to hit top form at the year-ending World Cup in Qatar following their shock first round exit in 2018, their earliest in the tournament in 80 years, they next play Italy on June 14 while Hungary travel to England.
"We did not play fast enough up front. We just made too many mistakes and we have to be satisfied with the result," Flick said.
"We are in a development process. It was clear when we started this in September there might be setbacks.
"We have to draw our lessons from this game. Hungary defended well. We were missing a bit of conviction in our game. We wanted three points, we did not get them and we are disappointed."
The hosts took a surprise lead in the sixth minute when Germany goalkeeper Manuel Neuer punched a Roland Sallai header away but Zsolt Nagy drilled the rebound past the keeper and into the roof of the goal.
Germany's Hofmann, who had also scored in their 1-1 draw against England on Tuesday, levelled only three minutes later, latching onto a deep, pin-point cross from Nico Schlotterbeck to round the keeper and slot in.
Hofmann should have added another in the 70th when he again charged through but instead of finishing the move himself, he attempted to lay it off for Timo Werner before his assist was intercepted in front of goal.
The Germans looked far from sharp up front, clearly missing a natural finisher with Werner struggling to create any real chances.
Neuer was kept busy until the end, making several more saves to keep them in the game. Hungary had seven attempts on target compared with just one from the Germans