The incident happened shortly before midday south of the airport between Gatwick and Haywards Heath and Horsham.
Gatwick Express said all lines remained closed at around 2pm, adding trains would likely be cancelled or diverted until at least 5pm.
Southern Rail, Thameslink and Great Western Railway services to the airport were also affected.
Passengers travelling with Gatwick Express, Southern and Thameslink have been advised to delay their travel to the airport until later in the afternoon with trains currently unable to run between Gatwick, Haywards Heath and Brighton.
This is affecting southbound services from London Victoria, Peterborough, Cambridge and Bedford to the airport, and northbound services from Brighton, Horsham, Southampton and Portsmouth.
Those travelling on Great Western Railway services to Gatwick will see their trains terminate at Redhill.
Tickets are being accepted on other reasonable routes and bus services.
Passengers have been warned alternative routes could extend their journey times by as much as an hour.
A "very limited" replacement bus service will operate between Gatwick, Three Bridges and Haywards Heath and as expected to be "very busy".