A Givealittle page has been set up to support the family of Kymani after she fell and sustained the injury on a school ice-skating trip at Alpine Ice Sports Centre on Brougham St.
The Haeata Community Campus student is understood to be on life support at Christchurch Hospital.
"This is a parent's worst nightmare - sending your child to school and to never return home," the Givealittle page said.
"Her parents, brothers, sisters and whanau are devastated. Kymani was a beautiful girl only 13 years old.
"As this is (an) unexpected tragedy, any funds would be gratefully appreciated and will go towards preparing for what comes next."
Emergency services were called to centre just after 11am on Tuesday.
St John said two ambulances and a rapid response vehicle were sent to the scene.
The centre was closed on Tuesday out of respect for the student but reopened on Wednesday.
Her great aunt, Lannie Belle, told chrislynchmedia.com the schoolgirl was on life support in hospital.
The girl's aunt Joanne Tusa told Chris Lynch Media the Givealittle page was set up to alleviate some of the stress her parents will have to endure in the days ahead.
Haeata Community Campus principal Dr Peggy Burrows told The New Zealand Herald the school had not had confirmation on her status.
She said the incident happened on an "EOTC" (education outside the classroom) trip.
"We understand that many whānau and ākonga will be affected by this uncertainty and by this tragedy," Burrows told the Herald.
"We will update our school community as soon as we have an official notification.
"Our thoughts and prayers are with the… whānau at this time."
The Ministry of Education addressed the incident in a statement this morning.
"We are deeply saddened by the tragic news and our thoughts are with the family and school community. Our traumatic incident team is available to support the school for as long as needed."