Southern Rail reported the incident on their Twitter account at 4.56pm on Tuesday [May 3] evening.
Southern's statement on social media said: "It is with great sadness that we report a person has been hit by a train between Worthing and Hove.
"All lines are blocked between these stations whilst the emergency services work to deal with this incident.
"You will want to allow up to 60 extra minutes to complete your journey between Worthing and Hove this afternoon and into this evening.
"If you are currently on a train which has come to a stand, please listen out for onboard announcements or get in touch directly.
In an update posted on Twitter at 6.40pm, Southern said: "All lines have now reopened, however we are currently unable to call at East Worthing.
"Delays and cancellations can still be expected until at least 22:00 this evening - this is whilst our Control teams work to recover the advertised timetable."
Tickets are being accepted on Brighton & Hove Buses between Brighton and Shoreham, and Stagecoach Route 700.
A limited rail replacement bus service is operating from Brighton at approximately 6.20pm, and Worthing from approximately 6pm.
Tickets are also being accepted on Southwestern trains between Portsmouth Harbour, Southampton Central and London Waterloo.