Bayern's Mario Gomez netted the winner in the 88th-minute on Tuesday at the Allianz Arena to seal Munich's 2-1 victory over Real in the first-leg of their semi-final with the return leg in Madrid next Wednesday.
But Real had a nasty surprise just before kick-off as two pairs of boots and two jerseys belonging to Madrid star Cristiano Ronaldo were stolen from the Madrid dressing room at the stadium.
A pair of boots belonging to Real's Germany midfielder Mesut Ozil were also taken.
Real have pointed the finger at Bayern, who have contacted the police to clear up the matter.
The crime may prove tricky to solve as there is no video camera surveillance in the changing rooms at the Allianz Arena.
"We are now trying to look at who can give us advice in the matter," police spokesman Wolfgang Wenger confirmed to news agency SID. "We are in contact with Real."
According to Spanish daily sports paper Marca, Real have already complained to European football's governing body UEFA.