Waters appeared on stage at Berlin's Mercedes Benz Arena this month wearing a black leather trench coat with a red armband showing two crossed hammers instead of a swastika.
He was dressed as the character Pink from rock opera The Wall during a performance of the song In the Flesh.
Berlin police spokesperson Martin Halweg told the Guardian: “An investigation has been opened over the costume displayed at the concerts on 17 and 18 May.”
Displaying Nazi symbols is illegal in Germany, although some exceptions exist for educational or artistic purposes.
Waters has since released a statement addressing the controversy.
He says: "My recent performance in Berlin has attracted bad faith attacks from those who want to smear and silence me because they disagree with my political views and moral principles.
"The elements of my performance that have been questioned are quite clearly a statement in opposition to fascism, injustice, and bigotry in all its forms. Attempts to portray those elements as something else are disingenuous and politically motivated.
"The depiction of an unhinged fascist demagogue has been a feature of my shows since Pink Floyd's The Wall in 1980.
"I have spent my entire life speaking out against authoritarianism and oppression wherever I see it. Regardless of the consequences of the attacks against me, I will continue to condemn injustice and all those who perpetrate it."
Waters could also be in hot water over his use of Anne Frank's name in a segment featuring activists killed by authorities. Frank was murdered in a Nazi concentration camp during the Second World War. Her name is trademarked by the Anne Frank Foundation.
He says: "When I was a child after the war, the name of Anne Frank was often spoken in our house, she became a permanent reminder of what happens when fascism is left unchecked. My parents fought the Nazis in World War II, with my father paying the ultimate price."
Waters recently won a legal battle with authorities in Frankfurt, after local authorities overturned the city council decision to cancel his upcoming show at the Festhalle concert hall. The show will now go ahead as planned tomorrow (May 28).
pic.twitter.com/RdxCXZY0GnMay 26, 2023