All lines are blocked between the stations while emergency services are on the scene, a spokesman said.
He added: “It is with great sadness that we report a person has been hit by a train between Horsham and Arundel.
“Services between London Victoria and Bognor Regis / Portsmouth Harbour / Southampton Central will be cancelled by this incident.
“If you need to travel to Barnham / Bognor Regis from London, we advise you to travel to Brighton and change trains there.
“South Western Railway will accept tickets between Portsmouth / Southampton and London Waterloo via Guildford.”
Those services will have a reduced capacity, as South Western has been affected by a landslip on their network, Southern said.
A spokesman added: “If you require stations between Horsham and Arundel, we have requested rail replacement buses to operate and we will provide a further update once the buses are in place.
“If you have not yet started your journey then please delay travelling until later as we currently cannot run trains between Horsham and Arundel.”
Southern said anyone using the following stations should delay their journey: