Paramedics rushed to the station, two stops before Waterloo for South Western Trains, at 8am on Thursday but the person was pronounced dead at the scene.
Delays caused by the death would last until 2.30pm with reports of passengers being stuck on trains, South Western Rail said.
A spokesperson from South Western Railway said: “We’ve been advised that emergency services are dealing with an incident between Clapham Junction and London Waterloo.
“Trains may be cancelled, delayed, or revised because of this problem.”
British Transport Police officers are currently working to identify the deceased and inform their next of kin.
A BTP spokesman said the force was called to Queenstown Road station following reports of a casualty on the tracks.
He said: “Paramedics also attended, and sadly a person was pronounced dead at the scene. Officers are currently working to identify the deceased and inform their next of kin.
“The incident is not being treated as suspicious and a file will be prepared for the coroner.”