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A tree which has fallen on the track near Sole Street station is preventing trains getting to London from Medway and stations in east Kent including Faversham and Ramsgate.
Southeastern Railways says the tree came down in the high winds and rain battering the county this morning.
It means that trains are not able to get to their final destination at London Victoria.
Southeastern spokesman Becky Endacott said: "The driver will try to move the tree, but if he is unable then chainsaw operators will have to cut it and then remove it.
"We are expecting them to arrive at the scene at just after 9am."
Southeastern forecasts that delays may last until 10.15am and advised passengers to check its website and social media pages for up to date information.
Another tree fell on the line at Dartford early this morning, but has now been removed.