The incident is likely to cause major disruption for many people on their way to work.
Vauxhall, with a rail station, Underground station and large bus station is an important transit point for those traveling from the south to other parts of London.
South West Trains said passengers should take alternative routes.
"Police have cordoned off a significant area this includes Vauxhall Rail, Bus and Underground stations. Trains are still running into and out of Waterloo but will not stop at Vauxhall station to set down or pick up passengers," its website said.
The Vauxhall area has been earmarked as a major development site.