Network Rail said the empty train had passed a red signal outside the station, activating an automatic derailment on Thursday. Overhead power lines also came down.
Operator GWR expects to run only half its normal service on Friday morning.
Network Rail said a limited service would run to and from London Paddington until the end of Friday.
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No Heathrow Connect service will run, but the Heathrow Express service will run every 30 minutes and Heathrow Connect tickets will be accepted.
A Great Western Railway (GWR) spokesman apologised for the disruption and said: "At the moment, we expect to be able to run around half our normal service in to and out of Paddington on Friday morning.
"We hope this will improve as further progress is made and we would ask customers to check before travelling.
"Passengers should expect GWR and alternative trains to be much busier than usual, particularly with additional people travelling to Ascot."
GWR said there was a reduced train service between Paddington and Reading.
It said the train had derailed in a siding, resulting in damage to infrastructure.
No passengers were on board when the train derailed and there were no injuries.
A Network Rail spokesman said: "Our engineers are working around-the-clock to repair significant damage caused by this incident.
"We are working to get things back to normal as quickly as possible and to minimise the inconvenience for passengers."
London Fire Brigade said it had been called to the station at 18:22 BST.
A statement said: "There was one person on board at the time of the incident who left the train before the brigade arrived.
"When crews arrived, they checked there was nobody trapped or left on board and once certain the scene was safe handed the incident back over to Network Rail."
Passengers have taken to social media to describe their frustration at the delays.
Azzy tweeted: "Can't get to Cornwall tonight then because I'll miss my connection at Plymouth", while Tanbir said: "@GWRHelp stuck on the train into #londonpaddington going to miss an event I've paid for, really annoyed!"
Passengers travelling through London Paddington are facing continued disruption after a train derailment.