Disruption is expected until around 3.15pm, Southern, which runs the route, said.
Rail replacement bus services have been drafted in.
On its website Southern said: “Police dealing with an incident near the railway between Hastings and Ashford International means some lines are blocked. Trains running between these stations may be cancelled or revised to start or terminate at Hastings.
“Stations between Three Oaks and Ashford International will not be served.
“A police investigation was being carried out near the railway between Ore and Winchelsea yesterday.
“Due to the complexity of the operation, more time is needed by the officers on site. Part of this investigation cannot be done with trains running past the area.
“Buses will replace a number of trains on this route. As a result, we expect your journey will take at least 30-45 minutes longer than usual.”
Southern said the following buses will operate:
* 12:25 Ashford International to Hastings
* 12:27 Hastings to Ashford International
* 13:25 Ashford International to Hastings
* 13:40 Hastings to Ashford International
* 14:25 Ashford International to Hastings
Southern added: “Any replacement buses for Three Oaks will serve the Southern replacement bus stops on the A259 at Guestling Thorn.
“Buses for Winchelsea will serve the Southern replacement bus stops in the centre of the village, rather than near the station.”
The investigation is being carried out by Kent Police as part of the search into missing 34-year-old Alexandra Morgan.
On Tuesday (November 30), a 40-year-old man appeared in court charged with Alexandra’s murder.
Mark Brown, from Squirrel Close, St Leonards, did not enter a plea when he appeared at Lewes Crown Court. He was remanded in custody and is next expected to appear in court in February next year. A provisional trial date was set for May 9
A Kent Police spokesman said: “Officers are searching a section of railway track close to Westfield, Hastings as part of their investigation into the disappearance of Alexandra Morgan.”