The incident occurred during rush hour in the morning on a District Line Tube train as it pulled into Parsons Green station.
An explosion caused by a suspected "bucket bomb" on a London Underground train at Parsons Green is being treated as a "terrorist attack", Scotland Yard has said.
The London Ambulance Service said 18 people have been taken to the hospital.
Assistant commissioner Mark Rowley says a suspected Improvised Explosive Device is thought to be responsible for the blast.
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Several people are said to have suffered facial burns after the blast in a bucket towards the rear of the District Line train. Some commuters reportedly were trampled and suffered crush injuries in the rush to escape.
Scotland Yard's counter-terrorism squad, SO15, arrived at the scene at Parsons Green Tube station and took the lead in the investigation from the British Transport Police.
"Deputy Assistant Commissioner Neil Basu, the senior national coordinator for counter-terrorism policing, has declared it a terrorist incident," the Metropolitan Police said in a statement.
"It is too early to confirm the cause of the fire, which will be subject to the investigation that is now underway by the Met's Counter Terrorism Command. The station remains cordoned off and we are advising people to avoid the area," it said.
Downing Street said Prime Minister Theresa May was "receiving regular updates" on the situation.
"My thoughts are with those injured at Parsons Green and emergency services who are responding bravely to this terrorist incident," May tweeted.
However, many commuters were also injured in the chaos that followed as people panicked and tried to escape from the scene, resulting in a stampede at the station.
Metropolitan Police bomb squads and fire crews remained at the scene including London Ambulance's Hazardous Response Units.
"We have sent multiple resources to the scene including single responders in cars, ambulance crews, incident response officers and our hazardous area response team, with the first of our medics arriving in under five minutes," the London Ambulance said.
Eyewitnesses from shops outside the station had reported seeing people with facial injuries. Many have been told to stay in lockdown as police evacuated the area and placed a wide zone under a police cordon.
Passenger Chris Wildish told the BBC that he saw a bucket in a supermarket bag with "low-level flames coming out of it" by the door of the rear carriage.