The footage shows a group of men appearing to shout “du Zigeuner” – a slur used against gypsies during the Holocaust.
They then start chanting and one man can be seen raising his arms in the air as he sings.
It was taken on a three-hour flight from Berlin Schoenefeld to the Majorcan town of Palma on May 28.
Elisa Zenck claimed the men were drunk when they boarded the aircraft for the 11.20am flight.
Posting about the incident on Facebook, she called the journey the “worst flight ever”.
Elisa later told The Independent that other passengers “tried to get off the plane as soon as possible” after the flight landed in Palma.
“I talked to one of the cabin crew, and she said every plane from Berlin to Mallorca in the summer is like that,” she added.
A spokesperson for Ryanair said: “We sincerely regret any misbehaviour by a small group of passengers on board this flight.
“The group stopped singing when requested to do so by our cabin crew.”
Disruptive passengers on flights are on the rise, with 413 reported in 2018, up by 100 per cent in 2015.
An easyJet passenger was filmed being bundled off a plane by cops after allegedly locking himself in the loos.
And a “drunk” man was booted off a Ryanair flight after allegedly abusing hen do and staff.