Ryanair flight FR7312 was flying from Dublin to Zadar in Croatia when the incident occurred.
A loss of pressure in the cabin meant the plane was forced to make an emergency landing at Frankfurt airport.
Oxygen masks fell as the plane descended thousands of feet, dropping 26,000 feet in just seven minutes according to flight tracking website Flight Radar.
According to Sky News, German police explained that 33 of the passengers out of 189 were taken to the hospital.
Some suffered from bleeding ears due to the loss of pressure, and others decided not to carry on with their journey.
Passenger Sarah McGarry told the Irish Times: “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’.
“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.”
Another passenger said: “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.”
Other passengers blamed the airline for not taking care of them after the incident.
A lack of food was noted, with a Twitter user saying only 100 McDonalds burgers arrived for 189 passengers in the morning.
Others said they had to sleep at the airport on the floor or with military camp beds.
Mrs McGarry declined medical treatment as she stated that she was not guaranteed she could make her replacement flight if travelling to the hospital.
She was one of the passengers who suffered with eardrum problems afterwards.
A Ryanair spokesman said: “Customers were provided with refreshment vouchers and hotel accommodation was authorised, however there was a shortage of available accommodation.”
Ryanair told Express.co.uk: “This flight from Dublin to Zadar (13 July) diverted to Frankfurt Hahn due to an inflight depressurisation. In line with standard procedure, the crew deployed oxygen masks and initiated a controlled descent.
“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 boarded a replacement aircraft which departed to Zadar the following morning and Ryanair sincerely apologised for any inconvenience.”
Another flight this week was forced into an emergency landing after an Air China pilot attempted to vape in the cockpit.
Despite trying to turn on the air ventilation, he instead turned off the air conditioning.
This meant the oxygen levels were lowered, triggering an alarm and a drop from 6,000m to 3,000m as oxygen masks fell.
An investigation has been launched as it is currently illegal to smoke e-cigarettes on a plane.
No-one was injured during the flight.