The schoolgirl was rushed to hospital after she suddenly went into cardiac arrest. She was pronounced dead shortly after.
Police and ambulance crews were called to Putney Leisure centre on Dryburgh Road at 2.46pm.
The child’s next of kin have been informed, and enquiries are still ongoing.
There remains a crime scene in place, although the leisure centre has been reopened.
Police are treating her death as “unexplained”, and are trying to work out the circumstances behind the tragic situation.
A London Ambulance Service spokesperson said: “We were called at 2.38pm to reports of an incident at Putney Leisure Centre.
“We sent a number of resources including an ambulance crew, an advanced paramedic, two medics in fast response cars and an incident response officer.
“We treated a patient at the scene and took them as a priority to hospital.”
The tragedy comes just a couple of months after a young boy suffered a cardiac arrest at a soft play centre in Walsall, near Wolverhampton.
ON February 1, an eight-year-old boy died following a heart attack at the Crash Bang Wallop play centre on Lindon Road.
Cardiac arrest is defined as when your heart stops pumping blood around your body, leading to your brain lacking the oxygen it needs to function.
While it is very unusual, cardiac arrest in children can sometimes be caused by undiagnosed genetic heart conditions or defects in their arteries that do not show symptoms until it may be too late.
Doctors recommend regular check-ups and an awareness of one’s family history with heart diseases as methods to help prevent these from happening.
Chest pain during exercise, fainting or irregular heart beats are regarded as possible signs a child may have a heart condition.