Winds gusting between 70 kilometres and 100 kilometres an hour were recorded in the Swiss plateau and exceeded 160 km/h in parts of the Alps, the ATS news agency reported.
A 75-year-old man died in Andelfingen in the canton of Zurich when a tree fell on his car as he was driving on a road through the woods, cantonal police said.
The victim died before emergency rescue workers could extricate him from the vehicle.
Elsewhere, a 77-year-old cyclist was injured after being struck by a trampoline that blew off the balcony of an apartment building in the municipality of Kriens in the canton of Lucerne, ATS said.
A 57-year-old woman received minor injuries when a tree fell on her car in Bubikon in the canton of Zurich.
Police in the canton responded to 100 calls for assistance during the storm, which originated in northern Europe.
Niklas was blamed for at least three deaths in Germany, The Local Germany reported.
Saxony-Anhalt police said a man was crushed to death when a concrete wall blew down near Magdeburg in eastern Germany.
Two road maintenance workers were killed when a tree fell on their car in the western state of Rhineland-Palatinate as a result of the storm, police said.
The strong winds disrupted train service in parts of Germany and cut electricity to thousands of homes.
In Austria, a 63-year-old man died as he tried to fix his roof, while a nine-year-old girl was injured by a falling tree.
In Switzerland, several mountain railways cancelled trains, including the Matterhorn-Gotthard line between Andermatt in the canton of Uri and Disentis in the canton of Graubünden, ATS said.
The storm forced the closure of the cog railway to Mount Pilatus near Lucerne and various mountain cable cars.
Winds gusting up to 165 km/h were recorded at Crap Masegn in the canton of Graubünden.
Weather experts clocked winds at more than 105 km/h in Zurich.
A massive slab of copper from the roof a church in the city dislodged and fell, damaging three cars and the balcony of a nearby apartment building.
In Flawil in the canton of Saint Gallen the storm carried away part of the roof of a building storing chocolate.
Heavy rain following the strong winds struck the Jura region, causing flooding in villages in the cantons of Neuchâtel and Bern.
Niklas followed on the heels of another storm, Mike, which dumped a record amount of rain on areas of the Jura, MeteoNews said in a news release.