Travellers claim the flight fell by “a hundred feet” as it battled an electrical storm on its way to London.
The five hour journey was like “the most terrifying rollercoaster” for much of the way, says one passenger.
Father-of-four Alex Rayner said the plane had to circle over Stansted for two hours before it had to be diverted to East Midlands Airport.
He claims passengers were screaming, praying and vomiting during the ordeal.
The 38-year-old told The Sun: “I put my hands together and prayed for God to keep my children and family safe first.
“We kept plunging what seemed like a hundred feet and then went up again were being thrown about like a toy plane.
“One of the frightening things about the ordeal, which lasted five hours, was the engines would be screaming loudly before they edged back to a normal rate every time it hit an air pocket.”
The events company chief executive said the trouble began soon after takeoff and described the lightning as the most terrifying part.
Mr Rayner said: “There was lashing rain, huge streaks of lightning. Every ten seconds lightning went really close to the aeroplane and every time it struck it lit up the plane like something out of a horror movie.
“This broke everyone. It was like being on the most terrifying roller coaster. By the end of it people were screaming every time there was a bolt of lightning.
“The woman behind me was praying. One passenger was holding her talisman and kissing her cross.”
When the plane did come in to land at East Midlands, the pilot had to abort the first attempt due to the conditions.
Mr Rayner said: “We came in for a landing and we got to within 200ft off the ground and suddenly the pilot whacked on the engines and we took off again.
“Very calmly the first officer said, ‘The pilot has decided not to land at this time’.”
Mr Rayner said his knees “buckled” when he finally stepped off the plane once it arrived at London Stansted.
Ryanair apologised to customers for the circumstances caused by the unavoidable weather event, which occurred on July 18.
The airline said in a statement: “This flight from Ibiza to London Stansted was unable to land at Stansted due to thunderstorms.
“The aircraft diverted to East Midlands, where it landed normally and returned to London Stansted once the weather improved.
“Ryanair sincerely apologised to all customers affected by this weather diversion, which was entirely beyond our control.”
