She went into cardiac arrest and died in hospital about an hour after the accident in the children's playground. Police are investigating the collapse.
The park, in Tower Hamlets, London, remains closed.
Mile End neighbourhood policing team tweeted: "We would like to express our sincerest condolences to the family of Alexia Walenkaki, who tragically died in Mile End Park on Friday."
The Metropolitan Police and the Health and Safety Executive (HSE) are jointly investigating the death.
Post-mortem tests are due to take place on Wednesday.
Tower Hamlets Council said it would not comment while the police and HSE investigations were ongoing.
A spokesman added: "The council would like to extend its deepest sympathies to the family involved."
The 36ha linear park was developed at the cost of about £25m from 1998-2002 after being in existence since World War Two.
Funding of £12.3m was from the Millennium Commission, £1.6m from English Partnerships, plus money from charities and private sources. Cabe Space cited the park as a park that gave benefit to the local community in a 2005 report.