The faulty train is being repaired at East Putney, causing severe delays for commuters.
The disruption comes days after Putney Bridge closed for three months to traffic as part of a £1.5m repair programme.
This means buses, used by many as alternative routes into work, will be on diversion.
Transport for London said tickets are being accepted on local buses via any reasonable route and on South West Trains between Wimbledon and London Waterloo.
Many of the stations along the District Line are closed this morning.
There is a good service on the rest of the line.