England's Madueke, who joined the club from Chelsea in July, was playing in his second game since returning from a knee injury that sidelined him for over two months.
He returned to action on Sunday as a late substitute in the 4-1 derby win over Tottenham Hotspur before coming off the bench again in the Bayern game replacing the injured Leandro Trossard.
Madueke opened his Arsenal account in the 69th minute, turning in a cross from fellow substitute Riccardo Calafiori.
"I had a long injury, it was difficult, but today I made up for it. It's amazing," Madueke told Arsenal's website.
"It was a Champions League night, so it was perfect to get my first goal for the club and for the win on top.
"It's a perfect night."
The victory saw Arsenal maintain their 100% record in this season's Champions League while handing Bayern their first loss of the season in all competitions.
With Inter Milan losing, Arsenal are now the only team in the competition with a maximum 15 points.
"It's a massive show what we're producing at the moment, not just in the Champions League, but our domestic form. We need to continue at this level and just keep it going," the 23-year-old added.
"The level we're playing at now is incredible and we need to try and keep adapting, keep pushing boundaries. That's the only way we can stay there."
Arsenal, who lead the Premier League with 29 points, face London rivals Chelsea on Sunday.
