The incident at Tayto Park in Co Meath happened last night during an after-dark Halloween-themed event.
It is understood the stairs gave way inside a ‘House of Horrors’ attraction.
Gardaí were called to the park shortly after 8pm.
A Garda spokesman said: “Nine people were taken to hospitals around the area.”
There are no details of the injuries sustained.
A spokeswoman for the park at Ashbourne said those caught up in the incident were taken to hospital as a “precautionary measure”.
The Health and Safety Authority is investigating.
A statement from Tayto Park said: “Last night at approximately 8pm the lower portion of a permanent staircase leading to The House of Horrors gave way.
“The Tayto Park emergency plan was immediately put in place and the emergency services attended the scene. Nine people were transported to hospitals in the city as a precautionary measure to assess their injuries.
“The management of Tayto Park will co-operate fully with the investigation as the safety of our guests is paramount.”
The park was open again yesterday.
Rian O’Kelly said she visited the park with her 13-year-old sister and her two young friends.
The 25-year-old from Dublin said the stairway was in two sections and she had just stepped onto the middle landing when the stairs behind her “vanished”.
“We heard this big creaking noise and we thought it was part of the show, like trying to be scary, but then, next of all, people directly behind us just dropped and the whole staircase collapsed,” she said.
“Obviously everyone got really afraid and everyone started crying and screaming and stuff and running because we thought we were going to drop down as well, because we had just stepped off that staircase and everyone behind us just had gone,” she told BBC radio.
Ms O’Kelly described the incident as “very scary”
“It was a family event— there were grown men and younger children on the stairs. There was definitely a lot of people injured from it. We basically just saw everyone behind us just suddenly drop and they all landed on top of each other and the staircase completely gave way.
“All the younger children, and adults even, were screaming and crying. It really was very scary and quite ironic, that we were supposed to be going into a house of horrors,” she said.
The park at Ashbourne opened in 2010. It is also home to Ireland’s first rollercoaster and Europe’s largest wooden rollercoaster with an inversion.