According to news agencies, the mother cow was part of a herd of 65 grazing on alpine pastures near Davos in the canton of Graubünden when she attacked a hiker who was walking along a designated trail.
The incident was reported by the Südostschweiz paper and confirmed to news agency ATS by Graubünden police on Tuesday.
The hiker was uninjured.
After attempts to keep the cow away from the hiking path failed, it was decided that the animal presented a danger to the public and should be put down.
Some 16 other cows in the herd will be brought down from the pasture on Wednesday since they are also deemed aggressive, said ATS.
Hikers often encounter cattle on trails throughout the Swiss Alps.
While attacks are rare, they can occur, especially when the herd contains calves.
In 2015 a 77-year-old German tourist was trampled to death by cows while hiking near Laax, in the Graubünden.
As a result, earlier this year the Laax area erected fixed fences along hiking trails that pass through fields containing cattle, to prevent further tragedy.
Hikers are advised to stick to designated trails, keep a good distance from cows and not turn their backs to them.
Dogs should be kept on the leash.