The German branch of the feminist group Femen posted a video on its Facebook page showing two activists mounting the stage during an appearance by Allen, who plays the clarinet, with his New Orleans jazz ensemble late Tuesday in the northern port city of Hamburg.
Their bare torsos covered in writing attacking Allen, the demonstrators shouted a passage from an open letter by Allen's adopted daughter Dylan Farrow published in The New York Times in 2014 outlining her father's alleged abuse when she was seven years old.
"They reminded the world and the the jazz-loving audience that Allen is not just a neurotic and charming director, musician and actor" but also an abusive parent, Femen Germany wrote.
In the video, the crowd can be heard booing the protesters as Allen, 81, is seen asking a fellow musician on stage what the women were shouting in German.
Security guards then yanked the women from the stage and the concert resumed.
The incident occurred at Hamburg's spectacular new Elbphilharmonie hall, where G20 leaders including US President Donald Trump attended a concert last week.
A spokesman for the venue contacted by AFP confirmed the disruption but declined to comment further.
Local news website shz.de said that at the end of the concert Allen described the protest as "stupid" and said he and his band would return to the stage for a second planned performance Wednesday night.
The accusation that Allen abused Dylan Farrow, now 31, has long haunted the Oscar-winning director of "Annie Hall" and "Midnight in Paris".
Her brother Ronan and their mother, actress-activist Mia Farrow, have said they opted not to press charges in the 1990s due to Dylan's "fragility" at the time and prosecutors decided not to pursue the matter.
Allen later struck back with his own open letter, calling the accusations "ludicrous" and repeating his charge that Mia had "coached" his daughter during their acrimonious split.
The New York filmmaker was confronted with the issue again last year at the Cannes film festival, where his movie "Cafe Society" opened the glitzy event.
The same day as the premiere, Ronan Farrow published a column in trade magazine The Hollywood Reporter lashing out at the media for failing to ask hard questions about the allegations.
Asked by reporters in Cannes, Allen said he had "said everything I had to say about that whole issue" in his column.