The 12-year-old boy died having suffered serious injuries at the SnowDome in Tamworth on Friday evening.
Staffordshire Police said the boy's family were being supported by officers and that a man was also treated for injuries.
In a statement, bosses confirmed that the SnowDome will remain closed while they "cooperate fully" with the investigation into the death.
The statement said: "The SnowDome is to remain temporarily closed following the tragic death of a child on Friday evening. The directors and staff are deeply shocked by what happened, and our thoughts and prayers are with his family at this terrible time.
"An investigation is currently being carried out by the authorities, and we are giving it our full cooperation. We are unable to reopen until their work has been completed, but hope to be able to update you on the position in the very near future.
"If you have a booking affected by the closure, we will be in touch with you shortly."