The boy, 10, was found trapped under the structure at St Lucy's School in Wahroonga about 2pm on Wednesday.
Police said a rescue operation was attempted by Fire and Rescue NSW but the boy died at the scene.
His body was recovered on Wednesday night and police continued their investigations at the school on Thursday.
Police are investigating the death at St Lucy's School that educates children with disabilities.
The state workplace safety authority has launched its own probe into the incident.
"SafeWork's investigation is ongoing and no further comment can be made at this time," the authority told AAP in a statement on Thursday.
Flowers were left outside the school reception on Thursday in memory of the student.
Deputy Premier Prue Car said the education department was supporting the independent school after a "heartbreaking and horrific" incident.
"This has been an absolutely tragic accident," she told reporters.
"There is obviously nothing quite like the loss of a child."
The school, which will remain closed indefinitely, provides primary and high education for children with disabilities.
Established in 1938 as a school for blind children, St Lucy's specialises in catering to kids with a range of special needs, including those with intellectual disabilities, autism and sensory impairments.
Broken Bay Bishop Anthony Randazzo said the school had an important mission in the Catholic diocese by educating children living with a disability and supporting their families.Â
"My thoughts and prayers are with the family for the loss of their child and the community of St Lucy's who mourn the loss of a student and friend," he said.
"Meantime, I ask all in our community to join me in offering prayers at this very sad time."
The school described the death as tragic in a statement on Wednesday.
Staff were co-operating with police, a spokesman said.
"We ask for privacy and space for our staff and families to grieve at this difficult time as we remember our beautiful student," he said.
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