Nine fire engines were sent to the derailment, where there was one minor injury, according to police and the fire brigade.
‘Lots of screeching’
The train was the 04:54 commuter service from Basingstoke.
The line into London is now open and trains can run, but will be delayed for the rest of the day.
Jane and John, passengers on the last carriage of the train, spoke to BBC Radio London.
“We thought it was going to come off the rails totally and there was lots of noise, lots of screeching, lots of sparks, and John and I held on to each other and thought ‘we’re in trouble if it goes over’,” she said.
John said: “It felt at one point like it was going to tip, then it didn’t, and remarkably, no one was screaming or anything, everyone was pretty calm, but it felt like it came quite close.
“You could tell it was off the tracks”.
London Fire Brigade said it was called out at 05.54 GMT.
It tweeted: “Specialist urban search and rescue crews have corrected the rear carriage that derailed nr #Wimbledon train station and are helping passengers from the train.”
Crews from Wimbledon, New Malden and Mitcham fire stations attended and the brigade later said all passengers had been helped off safely.
British Transport Police (BTP) warned of “significant disruption”, tweeting: “Officers are attending a low-speed partial derailment of a train in the Wimbledon area. One person sustained minor injuries.”
The Rail Accident Investigation Branch said a team of its inspectors had gone to Wimbledon start gathering evidence on site.
London Ambulance Service said there were four minor injuries, but nobody needed to go to hospital.
The Rail, Maritime and Transport (RMT) union said the incident highlighted the importance of having guards on trains.