From Friday there will be no Waterloo & City line, while the Night Tube will not run until further notice.
And from Thursday, up to 40 London Underground stations that do not interchange with other lines will be closed until further notice.
London buses will operate fewer services, but still run at night, and everyone will be urged not to use public transport for anything other than essential journeys.
The announcements come as the UK death toll related to the virus rises to 104, with more than 2,600 cases confirmed. The capital has played host to around a third of the total deaths so far.
Mayor of London Sadiq Khan said: "People should not be travelling, by any means, unless they really, really have to. Londoners should be avoiding social interaction unless absolutely necessary, and that means they should be avoiding using the transport network unless absolutely necessary
"London will get through these extraordinarily challenging times, and ensuring the capital's critical workers can move around the city will be crucial.
"Frontline staff across our health and care service - as well as those ensuring Londoners stay safe and can access food and other essentials - should be commended for their hard work. We owe it to them to do whatever we can to help them do their jobs effectively.
"I'm urging Londoners to only use public transport for essential journeys. Everyone should follow this and the other advice to help keep themselves and each other safe."
Additional reporting by PA.
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