A 17-year-old boy charged with the attempted murder of the child was remanded at Bromley Youth Court after a short hearing on Tuesday.
The court heard the child sustained a bleed on the brain and fractures to his spine, legs and arms in the alleged incident.
The youngster, a French national, was airlifted to hospital after he was found on a fifth-floor roof at the gallery on Sunday afternoon.
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The child, who is in a stable but critical condition, had plummeted five storeys after allegedly being thrown from the 10th-floor viewing platform.
The 17-year-old, who cannot be named for legal reasons, wore a grey jumper and sported stubble at the hearing.
He spoke to confirm his name, address, date of birth and nationality as British.
The court heard the six-year-old was at the gallery with his parents and they were on the viewing platform 'looking over the side and enjoying the view’.
The child is said to have walked a couple of feet away from his parents and was allegedly picked up and thrown over the edge in an action that was ‘carried out extremely swiftly and in one movement’, the court heard.
The suspect was apprehended by members of the public after the incident.
The teenager, who appeared in the dock, was remanded to youth detention accommodation until a hearing at the Old Bailey on Thursday.
Scotland Yard has said there is no link between the suspect and the victim.
Officers were called to the gallery at around 2.40pm and the child was treated at the scene before being flown to hospital by London's Air Ambulance.
Olga Malehevska was on the viewing platform with her four-year-old son when the alleged incident took place and described what happened as ‘absolutely terrifying’.
She said she saw a woman crying, shaking and shouting ‘oh my son, my son’.
The Tate Modern was the UK's most popular tourist attraction in 2018 after being visited 5.9 million times, according to the Association of Leading Visitor Attractions.