The 45-day old puppy developed symptoms of rabies on Friday after it was attacked by a ferret-badger in Haituan, a remote township in the south-eastern Taitung county.
A total of 124 ferret-badgers and a shrew were found to have carried the disease since May last year, the first outbreak since 1959.
Taiwan is now listed as a rabies-affected area by the Paris-headquartered World Organisation for Animal Health (OIE).
Tuesday's case prompted authorities to renew their call on domestic pet owners to inoculate their animals.
"There is no need for the pet owners to panic, but they have to make sure to get their dogs and cats to get a shot of vaccines against the disease," Edward Chao, the spokesman for the Bureau of Animal and Plant Health Inspection and Quarantine, told AFP.
As of now about 60 percent of the estimated 1.5 million pets on the island have been vaccinated against rabies, he said.
Only 10 countries and regions in the world are listed as rabies-free. Some 55,000 people die of the disease worldwide every year.
Symptoms in humans include seizures, partial paralysis, fever and brain inflammation, or encephalitis.
There is no known treatment to cure rabies once the infection has taken hold.