In Riehen, Basel-City, a woman was killed by a falling tree on Thursday morning, according to cantonal police.
In some exposed areas gales reached storm force, SRF Meteo reported, with alpine peaks recording gusts of 110 to 156 km/h.
In low-lying areas winds were gusting up to 100km/h.
The Luzerner Zeitung reported that around 3,200 homes in the Wolhusen and Entlebuch region were without power as a result of the storm.
At Zurich airport there was disruption to around 20 flight take-offs.
20 Minuten reported a spokesperson for Swiss International Air Lines as saying that a number of flights were delayed because the strong winds meant de-icing machines could not be used.
The storm also brought disruption to some train and ferry services.
The Basel-Rheinfelden was partly closed in the early morning after an uprooted tree fell on the lines.
Storm warnings are in place at airports and harbours.
According to the weather news website, the storm reached its peak on Wednesday night.
After a lull during Thursday it is expected to gather strength again overnight with its effects being felt until Friday morning.
Zubin also brought fresh snow to northern and eastern Switzerland early on Thursday.
During the day snow is expected at an altitude of above 600 metres.
Meteorological service Meteoschweiz is forecasting up to 40 centimetres of fresh snow.