It broke out in signalling cables underneath one of the platforms at about 03:00 BST.
The power has been isolated to the area and as a result South West Trains into Waterloo are severely delayed.
Services on the Hounslow loop and via Richmond and Kingston are not running and the bus station at Vauxhall has also been closed.
London Fire Brigade station manager John Ryan said: "Once the power was isolated firefighters quickly got to work to tackle the fire.
"We're currently assessing how much electrical cabling has been affected and damping down pockets of fire."
A fire on the tracks at Vauxhall station in London is causing major disruption in and out of the city.