The law came into effect Saturday, two years after it was passed by parliament -- a period meant to prepare shelters for the ban.
But during the wait, animal lover Chien Chih-cheng took her own life with euthanasia drugs, reportedly upset at having to kill animals at the shelter she worked at.
Reports at the time said Chien was called a "butcher" by activists.
Her death sparked calls for authorities to improve conditions for animals and staff at shelters.
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"Animal protection in Taiwan has moved towards a new milestone," the association's executive director Ho Tsung-hsun said in a statement.
But Taiwan's Council of Agriculture warned the ban would lead to a deterioration in the quality of shelters through a surging intake or it may discourage the capture of strays.
"It's impossible for there to be no problems," said Wang Chung-shu, deputy chief of the animal husbandry department, according to The China Times.
He said Taiwan's ban was "quite idealised", adding that manpower was a problem because the vet's suicide had had a "chilling effect" on the sector, according to the report.
Last year, 12.38 percent of the 64,276 animals in public shelters were euthanised, according to official statistics.
That compares with 94,741 animals in shelters in 2014, of which 26.45 percent were put down.