In a post on social media, Southern said all lines between these stations are blocked and replacement buses are in operation.
There is also a communications issue in the area, affecting how trains show on the customer information screens, Southern said.
A Southern spokesman said: "Services are currently unable to run between Three Bridges and Horsham in both directions.
"Services which run between London Victoria and Portsmouth Harbour, Southampton Central and Bognor Regis will divert either via Hove or Dorking where possible.
"Replacement buses have been requested. Buses have been confirmed for Three Bridges and currently on route. We are still awaiting confirmation on the Horsham buses at this time.
"When these buses arrive, they will not run to schedule, so please talk to station staff for details."
Disruption is expected until 9pm.