Pictures from the scene show what appears to be a white bucket on fire inside one of the train cars, which is believed to be connected to the explosion.
"My thoughts are with those injured at Parsons Green and the emergency services who, once again, are responding swiftly and bravely to a suspected terrorist incident", May said in a statement. "I will be attending the emergency COBRA meeting in Whitehall this afternoon with the Prime Minister", Mirror quoted London Mayor Sadiq Khan as saying.
London mayor Sadiq Khan, said the city "utterly condemns the disgusting individuals who attempt to use terror to harm us and destroy our way of life".
It is also being reported that people were initially told not to leave the station before an evacuation took place.
Train services between Earl's Court and Wimbledon on the District Line were immediately suspended. The device did not detonate fully, police confirm.
The Metropolitan and British Transport police forces rushed to the scene.
Passenger Chris Wildish told BBC Radio 5 live he saw a bucket in a supermarket bag with "low-level flames coming out of it" by the door of the rear carriage.
"I was on (the) second carriage from the back".
Large numbers of police, ambulances, and fire trucks are in the area, which has been cordoned off by armed police officers. Police are treating what they originally called a "security situation" at the southwest station at Parsons Green as a terrorism incident.