Just after 4pm the slip smashed through a bedroom wall, Southern fire communications shift manager Karl Patterson said.
The family had left the home, but it was not known if other properties were being evacuated, Mr Patterson said.
The Marlborough District Council said the heavy rain in Picton caused overflows at several points in the town's sewerage system.
The sewage pumping station in Dublin Street was overflowing into Waitohi Stream and sewage was overflowing through the Kent Street drain into the stream. The Picton Marina was getting overflow from three points in the sewerage system.
The council said Picton's Waitohi Stream was running very high, causing discolouration in the harbour.
Members of the public were reminded to follow safe hygiene practices if they come into contact with dirty water.
Meanwhile, a slip closed the Rimutaka Hill Road north of Wellington, caused major traffic delays yesterday afternoon.
The road had reopened by 6pm, but NZ Transport Agency regional performance manager Mark Owen said motorists needed to take care on the road.
"We are advising motorists to drive with care as conditions are challenging and continued rain could lead to more slips."
MetService spokesman Daniel Corbett said the departing low covering some of the country would have a "slight sting in its tail" with numerous thunderstorms, persistent rain and southerly gales.
Today was looking much drier and brighter for most of the country, he said.
However, a fast-moving trough is on its way and was likely to spread another spell of wet weather along the West Coast of the South Island this afternoon, with some spilling over into the Otago and Canterbury lake and river catchments.
Severe northwest gales were also expected in parts of Canterbury, Marlborough, Wairarapa and Wellington.
MetService had issued a Severe Weather Warning for this event, Mr Corbett said.
The worst of the rain and wind should weaken as the trough pushes north over the rest of the country this weekend.
For the annual Lake Taupo cycle challenge - set to take place on Saturday - the weakening trough was likely to bring thickening cloud and some rain and wind later in the day, Mr Corbett said.
A new high from the Tasman Sea would bring mainly dry, settled weather for the start of next week.
