Public Health England (PHE) said the case was "rapidly detected" after the death of the animal last week and movement restrictions are in place in the area.
All of a sudden, unexplained deaths of cattle are investigated for anthrax, and hundreds of samples are examined in the UK each year.
Mike Wade, deputy director of health protection for PHE South West, said: "We are aware of a confirmed case of anthrax disease in a cow in the Westbury area of Wiltshire.
"Anthrax is a bacterial disease which primarily affects grazing animals, although all mammals are susceptible. This is the first case in an animal since 2006 and human cases of anthrax are very rare - with the last case occurring in 2008."
Wiltshire Council spokesperson said: "We worked with our partners both locally and nationally and swift action was taken to deal with the immediate risk.
"We know any risk is low; however, as you would expect, we are taking this very seriously and we will be doing everything in our power to support the national and local experts to keep Wiltshire safe."
Anthrax is caused byBacillus anthracisand can be deadly but it struggles to spread from one animal to another or between people.
It can be treated with antibiotics but treatment needs to start soon after infection.
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