Heavy rainfall, up to 50mm, and winds of up to 40mph are expected.
In a statement Southern Rail added: “The area that will be most affected by these restrictions is Holmwood following the landslip that happened there two weeks ago. A speed restriction of 5mph will be introduced along the one mile stretch of line through the area from the start of service Monday morning. Daily inspections have been taking place and will continue through this period.
“The services that will be affected by this are the Horsham to London Victoria via Dorking services.”
It stated fewer services will run from Horsham towards Epsom or Sutton and that passengers may find it quicker to travel to London Bridge or London Waterloo and continue journeys from there.
It added: “The 07:20 Horsham to London Victoria will be diverted via Gatwick Airport. A rail replacement bus will be in operation to cover this service calling all stations as far as Leatherhead where there are frequent services to London.
“Network Rail will be proactively working overnight and throughout the day to ensure pumps and drainage are in place and in full working condition as well as ensuring that enhanced checks are taking place in areas that have higher risk of tree fall and landslip to prevent potential disruption to the rail network.”