Evha Jannath fell out of a circular boat on the Splash Canyon attraction during a school trip to Drayton Manor Theme Park in Staffordshire on Tuesday.
The pupil, from Leicester, was rescued from the water and taken to hospital but pronounced dead a short time later.
A statement released by Evha's family said their "world was torn apart" following her death.
They described her as "a beautiful little girl who was full of love and always smiling".
"Words cannot describe the pain and loss we feel, we are devastated that we will not see our beautiful little girl again."
Police said it was an "extremely difficult time" for Evha's relatives and the force was providing support from specially trained officers.
The theme park is to remain closed for the day as "a mark of respect". The girl's school, Jameah Girls Academy in Leicester, is also closed.
In a statement, the Islamic day school asked that the Year 6 pupil's family and school community be given "time to grieve".
Head teacher Erfana Bora said Evha was a "lovely, sweet-natured girl [who] was loved by everyone at the school".
"We are trying to make sense of this terrible tragedy. Our thoughts and our prayers are with Evha's family," she added.
Drayton Manor Theme Park has been closed for the day as a "mark of respect"
Splash Canyon opened in 1993 and features up to 21 boats
Prayers have been said for the girl at the Jameah Mosque in Leicester.
Staffordshire Police said a Health and Safety Executive investigation had begun.
The ride, which opened in 1993 and features up to 21 boats each with a capacity of six people, closed following the incident at the park near Tamworth.
It offers a "a wild ride" with "fast-flowing rapids" and riders must be at least 0.9m (3ft) tall to board, although those under 1.1m must be accompanied by an adult.
On Tuesday, park company director George Bryan, whose grandfather opened the site in the 1950s, said he was "truly shocked and devastated" by the death.
West Midlands Ambulance Service said it sent paramedics by land and air to the site.
A spokesman said crews discovered a girl "with serious injuries who had been rescued from the water by park staff".
She was flown to Birmingham Children's Hospital but was pronounced dead a short time later.
Emergency services were sent to the park after reports someone had fallen in the water on Splash Canyon
Zainab Mohammad said her 16-year-old sister, who was on the same school trip, was devastated.
"She came home, she spoke to mum and dad and she just went upstairs.
"She was devastated. She didn't want to talk about it. The school is not very big, everybody knows each other.
"We don't know what the cause is but what we really want is for the family to be able to grieve.
"A family member has been ripped from their family and it's a big loss. Everybody is in utter shock, there are no words."
The girl's school has also shut for the day and pupils and staff are being supported
Prayers have been said for the girl at the Jameah Mosque in Leicester
Vikki Treacy told live her son fell in the water on the same ride in 2013.
She said Patrick, who was 10 at the time, "sort of stood up" for a photo and toppled from the boat.
The mother, from Rugby, said: "When you are queuing up, the loud speakers are telling you the safety instructions, like please stay seated.
"[But] they're getting excited and giddy, they're not listening to a tannoy are they?
"[After he fell] I panicked and a woman... in the spectators' bit, hopped over a fence at the side and dragged him out.
"My son was in an area where the public could get to him. It's a dangerous ride. It really is.
"I'll never go back to the park. No way. Their aftercare was shocking."
Drayton Manor said it could not comment on the claims while the Splash Canyon investigation was ongoing.
A spokesman added: "The health and safety of our visitors is of paramount importance and we'd ask Vikki contacts us direct so that we can address her concerns."
Theme park enthusiast Ian Bell, who owns rollercoaster fan group Coasterforce, said rapids rides like Splash Canyon tended not to have seatbelts in case they capsized.
"They are fairly buoyant; I've never heard of one capsizing. They are very safe," he added.
Vikki Treacy (right) said son Patrick (left) fell in the water on the same ride in 2013
Health and safety lawyer Chris Green told BBC Radio 5 live he had been on the ride with his daughters and had never thought it could be dangerous.
He said the HSE would need to establish if the accident was work-related.
"They'd be firstly trying to understand from witnesses precisely how this has happened and that will determine whether it's them in conjunction with police, whether that's a report for the coroner or for other proceedings as well."
The death at Drayton Manor is thought to be the first at a UK theme park since 2004, when a 16-year-old girl fell from the Hydro ride at Oakwood theme park near Tenby, west Wales.
In June 2015, five people were seriously injured in a collision on the Smiler rollercoaster at Alton Towers, also in Staffordshire.
Mr Green said: "The Alton Towers scenario looked more perhaps as if something inevitably looked like it hadn't worked on the day. This one [at Drayton Manor] may be rather different."
Officials posted on social media on Tuesday that the park would remain closed