She died at Auckland's Tamaki College while her family was at a touch tournament about 2.30pm yesterday.
Mealamu's three-year-old nephew was also injured in the incident.
Family members and friends gathered at Luka Mealamu's home in Mangere last night, but were too upset to talk.
All Black coach Graham Henry has passed on a message of support to Mealamu from the team.
A Northern communications spokesman declined to say what the sporting equipment was but TV3 News said the girl was killed by a scrum machine.
The girl suffered extensive injuries and ambulance personnel were unable to revive her.
"Family members at the scene are understandably very distraught by the tragic circumstances," police said.
The Labour Department and police would investigate.
The girl's family had asked for privacy during their grieving period.
A St John Ambulance spokesman said the girl was dead when they arrived at the scene.
