The Blues, who were crowned Club World Cup champions in July, were back in Europe's premier competition for the first time since the 2022/23 season.
But it was a baptism of fire for Enzo Maresca's young side - eight of the starters were tournament debutants - at the Allianz Arena, with Bayern's experience ultimately showing through.
Maresca made four changes after Saturday's 2-2 draw at Brentford, as Cole Palmer came back into the starting line-up, alongside captain Reece James and full-backs Marc Cucurella and Malo Gusto.
The Blues started brightly but the Germans found the breakthrough on 20 minutes, when Trevoh Chalobah diverted a cross into his own net.