Southern Rail said that all lines were blocked due to the incident, which happened between Three Bridges and Brighton and was reported at around 3pm.
There have been widespread cancellations across Sussex, and journey times have been extended by up to 90 minutes.
In a statement on its website, Southern said: "There is currently no estimate available as to when lines will reopen, however, we anticipate trains will be disrupted until at least 7pm."
The condition of the person involved is currently unknown.
British Transport Police has been approached for more information.