They said they heard a "sudden bang" and the "air became cold" as oxygen masks fell from the ceiling and they thought they were "done for".
Passengers reported feeling intense pain in their ears and nausea as the aircraft dropped thousands of metres in less than a minute, until the plane levelled off and landed at Frankfurt-Hahn airport.
According to Flight Radar, it descended 8000m from 11,300m to 3000m in seven minutes.
Minerva Galvan Domenech from Spain told news website Spiegel Online on Saturday that passengers, some of them bleeding from their ears, mouth or nose, had to wait 45 minutes before being allowed to leave the plane.
Documenting the horror ideal on Twitter, she said it was one of the worst moments of her life.
"You are in the air and one moment after you are just falling in the sky, your ears burn, there is no air and your mouth taste like iron," she said.
Passenger Sarah McGarry said they were left in the basement of the Frankfurt airport after the landing.
"We get on the plane, we're flying and next of all the oxygen mask comes down, we're left in darkness for 15 minutes, there's no reassurance just people shouting 'emergency, emergency'," she told the Irish Times.
"There was a newborn baby and children on the flight, people are screaming and we don't know what's going on for 15 minutes … Then finally we're told that we're going to Germany."
Another told the newspaper: "It was really scary, there were three to four minutes (that felt like an hour) when the plane was falling fast and I thought we were done for".
Paul Wiseman said it was a nightmare flight, blaming cost cutting for their treatment.
"Overnight in military base camp beds — good old Ryanair style customer service," he said.
"Cutting costs and more profit for Ryanair all at the expense of customer safety."
German police said 33 of the 189 passengers on board were taken to a nearby hospital after complaining of headaches, ear pain and nausea. All were able to leave again by Saturday morning.
Passenger Conor Brennan told the Irish Times that "airport staff and Red Cross did their best to handle the situation, as Ryanair were nowhere to be seen."
"They really displayed a shocking lack of empathy for their customers, almost bordering on inhumane," he said.
Galvan Domenech said many passengers had to spend the night at the airport, some of them lying on the ground, according to Spiegel Online.
Ryanair said passengers received refreshment vouchers but there was "a shortage of available accommodation". Frankfurt-Hahn has long been a major base for Ryanair.
One passenger said Ryanair's treatment was appalling.
"100 McDonald's cheeseburgers arrived at 5 in morning for a plane with 189 passengers. Thank you Ryanair. No wonder your people are striking," he said.
"No accommodation, no food, people laying on floors in a military base, being told we could not leave the base … we are still in Frankfurt airport caged after 12 hours overnight with no sleep. Abhorrent treatment for people post trauma."
A replacement flight took some of the passengers to Croatia on Saturday while others went to Zadar via a chartered bus.
Ryanair said the flight was diverted because of "in-flight depressurisation".
"In line with standard procedure, the crew deployed oxygen masks and initiated a controlled descent," they said.
"The aircraft landed normally and customers disembarked, where a small number received medical attention as a precaution.
"Customers were provided with refreshment vouchers and hotel accommodation was authorised, however there was a shortage of available accommodation.
"Customers will board a replacement aircraft which will depart to Zadar this morning and Ryanair sincerely apologises for any inconvenience."
Ryanair has long been dogged by accusations of poor service and bad treatment of staff. Last week, Ryanair pilots in Ireland staged their first strike and two more walkouts are planned on July 20 and July 24.
