West Midlands Ambulance Service and Staffordshire Police were called to reports of the child being seriously injured during an activity in the SnowDome in Tamworth at around 6.35pm on Friday.
He died a short time later, emergency services added.
Staffordshire Police said the boy's family were being supported by officers and that a man was also treated for injuries.
Tamworth SnowDome confirmed it be closed for the rest of the weekend while an investigation into the boy's death is conducted.
Martin Smith, Chairman of SnowDome Ltd, said: "The directors and all of the employees extend their heartfelt thoughts and prayers and condolences to the family and friends of the young boy.
"For an evening’s activity to end so tragically is almost beyond belief and our sorrow is deeply felt.
"The company is in full co-operation with the investigating authorities and is providing complete and absolute assistance."
A West Midlands Ambulance Service spokesman said: "On arrival crews found a boy who had suffered very serious injuries.
"Staff worked on him providing advanced life support, but sadly, despite all of the efforts it was not possible to save him and he was confirmed dead at the scene."
Two air ambulances were sent to the scene.
Police said the Health and Safety Executive has been informed of the incident and asked people not to speculate about the incident or share images or footage.
A Staffordshire Police spokesman said: "Officers attended the location along with ambulance crews who treated a boy at the scene.
"Sadly, the boy, aged 12, died of his injuries shortly afterwards.
"His parents are being supported by officers. Our thoughts are with them.
"A man is also being treated for injuries.
"We would kindly urge people not to speculate about the incident or share any images/footage there may be.
"The Health and Safety Executive have been informed of the incident.
"Anyone who has information about the incident can contact us on 101 or via social media ref 665 of September 24."