MetService predicts snow on Monday evening and early Tuesday morning as low as 400 meters over the range of Fiordland and Southland.
A MetService spokesman said the snow would be brought by a front that is expected to travel to the far south of the South Island from the southwest during the day.
Besides snow, it was expected that it would bring rain to the southwestern parts of the South Island and some heavy waterfalls in the south of Fiordland.
Precipitation in the rain can approach warning amounts up to 90 mm in Fiordland, south of George Sound, from Monday morning to early Tuesday morning.
Residents are advised to stay abreast of the latest predictions in case a full warning or other areas are added, he said.