The obstruction is stuck under a train and current services have been held at Northfleet while the incident is dealt with.
Power to the tracks has been switched off.
South Eastern said: "Network Rail staff are on site and working to clear the obstruction. We're hoping to have the line clear and trains running as soon as possible."
Train tickets are being accepted at no extra cost on FastTrack bus route B between Gravesend and Dartford.
Network Rail Kent and Sussex said: "This is the opposite of everyone pulling together - someone dumped a mattress on the railway near Swanscombe and a train has hit it. We are trying to get passengers evacuated as soon as possible so please hang in there. As for whoever dumped the rubbish, words fail us."
Following this a train struck a bike on the tracks near Swanley.
Trains on the Maidstone East Line had been delayed, revised or cancelled as a result.
On Twitter, South Eastern stated: "The train has been declared fit and safe to move forward.
Once it has left Swanley station, we'll be able to resume running between Ashford and Maidstone East."