St John said they were called to the Alpine Ice Sports Centre on Brougham St, Opawa, about 11am.
"Two ambulances and a rapid response vehicle responded to the scene and treated and transported one patient to Christchurch Hospital in a critical condition."
Police directed any questions to St John but told Stuff someone appeared to have had a fall.
Fire and Emergency NZ staff were also called to the centre after reports of a medical event.
A staff member at the ice-skating rink told Stuff the centre has been closed for the day out of respect.
Stuff reported some employees at the centre appeared visibly upset following the incident.