Officers were called to Putney Leisure Centre on Dryburgh Road in south-west London at 2.46pm where the girl was reported to be in cardiac arrest.
The girl, a pupil at Hotham Primary School, was taken to hospital but died a short time later.
A school spokesman said: “Our entire school community has been left shocked, saddened and deeply upset at today’s tragic events involving a pupil from our school who has sadly passed away.
“Our thoughts and deepest sympathies are with her family as they come to terms with their loss and we will do all we can to support them and also our staff and all our pupils in the difficult days ahead.”
Read more: 10-year-old girl dies at Putney Leisure Centre after going into cardiac arrest