"This is of course a very sad and difficult time for our staff and tight knit school community who are pulling together to deal with this tragic event. Our collective thoughts are with the Kurth family at this terrible time of loss."
Ministry of Education head of sector enablement Katrina Casey said it was a sad situation for the family as well as for the school and its community and they are all dealing with it as best they can.
A traumatic incident team was working with the school.
"The team is helping the school to put systems in place so that those most affected have the right support if they need to call on it, and so that the day to day focus of the school returns to teaching and learning as soon as possible," Casey said.
"Returning to normal routines is helpful for children in these situations."
She said the deputy principal would manage the school while the principal took a period of leave.
A police media spokeswoman confirmed the child was believed to have died from a medical event and the death had been referred to the coroner.
A Fire and Emergency spokesman said they also attended to help ambulance staff and set up a landing site for the rescue helicopter.
A death notice in the Herald on Saturday said Ellie "passed away suddenly" and described her as the precious daughter of Jeremy and Anna and loved little sister of Brenna.
A death notice in today's Herald said she "passed away at school surrounded by people who loved her".
"To our beautiful little Ellie Minelli, why did this happen? We are so incredibly heart broken at the thought of life without you. You were so special to so many people and brought laughter and light to our lives every single day," another notice said.
Friends of the family have taken to Facebook and an online memorial page to describe her as fun and bubbly.
One commented that she was "the most cheeky, adorable, spontaneous lover of life".
Jeremy Kurth became the principal of the school which has a roll of just more than 100 students at the end of 2012.
In 2013, Ellie and her older sister Brenna were pictured handing over a large cheque worth $1700 to Kidz First at Middlemore Hospital which their mother Anna had raised to replace a stolen iPad.
Ellie had been having regular treatment at the hospital to treat a rare skin condition, the Matamata Chronicle reported.