Shortly before rush hour nine platforms were closed, leaving passengers stranded in the concourse.
It is thought the fire may have caused “significant damage” to a number of essential cables.
Network Rail said its engineers would work through the night to fix the damage, but services were likely to be disrupted on Thursday morning.
“We are very sorry for the disruption," a spokesman for Network Rail and South Western Railway said.
“A lineside fire this morning caused significant damage to some of the rail infrastructure in the Waterloo area, fully closing platforms 16-24," he added, “Trains will be delayed or cancelled until the end of service today and disruption is likely to impact services tomorrow morning.
“Passengers are strongly advised to check their journeys before travelling at http://www.southwesternrailway.com for ticket acceptance and service details.”
Trains between London Waterloo, Hounslow, Richmond, Strawberry Hill and Kingston were cancelled, while services between Waterloo and Windsor & Eton Riverside were diverted via Kingston.
Waterloo station this evening, nightmare! pic.twitter.com/D9NV3qrj9O— William Laven (@WilliamLaven2)July 17, 2019
Passengers were warned that services on other routes may also be subject to short-notice cancellations or delays.
Additional reporting by Press Association