A Waikato DHB spokeswoman said the patient was now in a stable condition in a general ward.
Hinuera Rugby and Sports Club posted a tribute to 13-year-old on Facebook saying it was "with incredible sadness that we learn of the tragic passing of one of our young club members".
"[The teen] was a fantastic captain, a true leader and an outstanding rugby talent who represented our club with pride and achieved at representative level," the club wrote.
"An amazing role model to his peers and our young junior rugby players. We were very lucky to have him as part of our club.
"Our thoughts, love and prayers go out to [the] family, long time members and supporters of our club. Our collective hearts are hurting so badly for you all."
The boy's last photo on Instagram shows photos of him waterskiing five days ago.
Many friends and family have posted on the images saying rest in peace and posting heart emojis.
Matamata College Principal Alan Munro said the school was shocked and saddened to hear of the accidental death of Year 9 Matamata College student.
"[The victim] was a positive all-round student with strengths academically as well as on the sports field.
"Well-liked by his peers and staff and his loss of life has hit our school and wider community hard," Munro said.
"The school is handling this tragedy as best we can, and our Incident Response Action plan has been actioned to support staff and students.
"Guidance staff have been on hand to support students and this will continue during the week ahead.
"Our thoughts and prayers are with the family during this difficult time as they are with the families of other boys involved in this tragic accident."
Matamata Intermediate School principal Debbie Currie confirmed the boy was a former student.
"We are devastated by the tragic loss and as a school, our hearts go out to his family," she said.
Maritime NZ said an investigation into the incident was underway.
