- In one scene Geldof plays a rock star hallucinating that he is leading a fascist rally.
- Police authorities have said that once the allegations have been reviewed, the matter will be passed on to the public prosecutor.
Police are investigating former Pink Floyd bassist Roger Waters after he wore what appeared to be a Nazi SS uniform during a concert in Germany.
Performing in Berlin on 17 May, Waters wore a long black overcoat with a red armband. He also aimed an imitation machine gun into the audience.
Germany bans displaying Nazi symbols - but the country's laws allow exceptions for artistic or educational reasons.
Waters said his performance was clearly to show "opposition to fascism".
Following the concert at Berlin's Mercedes-Benz Arena, German police spokesman Martin Halweg said: "We are investigating on suspicion of incitement to public hatred because the clothing worn on stage could be used to glorify or justify Nazi rule, thereby disturbing the public peace.
"The clothing resembles the clothing of an SS officer," he added.
Waters' jacket included a red armband with two black crossed hammers on a white circle, an outfit he has worn at previous shows dating back several years.
The symbols are similar to those appearing on costumes in the 1982 film, The Wall, based on the Pink Floyd album of the same name and starring fellow musician turned activist Bob Geldof.
In one scene Geldof plays a rock star hallucinating that he is leading a fascist rally.
Police authorities have said that once the allegations have been reviewed, the matter will be passed on to the public prosecutor, who will decide how to proceed.
During the Berlin performance, the names of several deceased people also appeared on a large screen.
The names included Anne Frank, the Jewish teenager who died in a Nazi concentration camp during World War Two.
Israel's foreign ministry later criticised the musician on social media.
"Good morning to everyone but Roger Waters who spent the evening in Berlin (Yes Berlin) desecrating the memory of Anne Frank and the 6 million Jews murdered in the Holocaust," it tweeted.
In a tweet on Friday, Waters wrote: "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... The depiction of an unhinged fascist demagogue has been a feature of my shows since Pink Floyd's The Wall in 1980."
Waters has also floated an inflatable pig marked with the Star of David at his concerts.
In recent weeks, the musician has been travelling to cities around Germany as part of his This Is Not A Drill tour.
However the performances have been controversial. Munich and Cologne tried to cancel shows after Jewish organisations such as the Central Council of Jews accused him of antisemitism.
Waters denies the accusations, and in a Facebook post this week he thanked those who had attended his shows in Germany.
He also paid tribute to the White Rose movement, a resistance group during the Nazi period.
"The fact that some in power in Germany and some at the behest of the Israeli lobby have attacked me, wrongly accusing me of being an antisemite, and have tried to cancel my shows saddens me," Waters said.
"Walking around Munich yesterday afternoon, I couldn't shake off the feeling that I was in the presence of Big Brother. It leaves a bad taste."
Waters is still scheduled to play his final concert in Germany on Sunday evening in Frankfurt. Demonstrations are planned outside the venue, however, after a legal attempt by the city to stop the performance failed.
A British MP has also called for Waters' gig in Manchester in June to be cancelled.
Waters has made several controversial comments in the past.
After Russia's full-scale invasion of Ukraine last year, he penned an open letter to Ukraine's first lady, Olena Zelenska.
In it, he said, "extreme nationalists" in Ukraine "have set your country on the path to this disastrous war".
In February, during a speech to the United Nations he repeated his controversial claim that Russia's invasion of Ukraine was "provoked".