Locals sell live dogs for meat in and around Yulin, China, as part of an annual festival in June.
If found guilty of deliberately causing harm to pets, including death, a person can now be sentenced up to two years in prison and fines ranging from $6,524 to $65,434, the Central News Agency reported.
Authorities will also be able to name and shame those who break the law.
But in mainland China, there is no law explicitly banning the eating or sale of dog and cat meat.
The amendment's sponsor, Kuomintang Legislator Wang Yu-min, said that while some localities already had measures banning dog and cat meat consumption, national legislation was needed. In addition to prohibiting residents from selling or using cats and dogs for food, the amendment bans residents from attaching leashed animals to motorized vehicles.
The law says individuals who eat or trade dog or cat meat can be fined between $1,640 and $8,200, CNN reported.
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Repeated offenders will face a maximum of five years in jail and a fine of 5million ($163,000) Taiwan dollars, lawmakers said.
The move on Tuesday is a landmark amendment to Taiwan's Animal Protection Act, and is the first of its kind in Asia.
The amendment came in the wake of several high-profile animal abuse cases in Taiwan.
Taiwan's president, Tsai Ing-wen, is a well-known cat lover, frequently posing with her two cats during her campaign. Last year, the Defence Minister made a public apology after a video showed soldiers hanging a stray puppy by its neck over a seawall and watching it struggle until it died.
Although accurate figures are hard to obtain, China is believed to be responsible for the majority of global cases of cat and dog slaughter.
Reactions to the latest law were mixed, with some islanders deeming it unfair that only cats and dogs had been chosen to enjoy better protection.
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