The fine also covers food products that contain parts of the animals, and offenders' names and photos may also be publicised, according to the report.
Under the amendment, those found to have deliberately harmed cats and dogs, resulting in their limbs being mangled or causing organ failure and death will also face a jail term of up to two years and a NT$2 million fine.
Presently, the maximum penalty is one year in jail and a fine of NT$1 million. The bill still has to be signed into law by the cabinet and presidential office before it will take effect.
Eating and selling dog and cat meat is already banned by local governments in some parts of Taiwan, but the law change will make it illegal throughout the island.
Opposition Kuomintang legislator Wang Yu-min had pushed for the change.
She said the amendment showed Taiwan was a progressive society on animal rights and could act as a reference for other Asian cities, Taiwanese news outlet Storm Media reported.
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Last October, Chan Ho-yeung, a former National Taiwan University student from Macau, was sentenced to 10 months' jail for killing stray cats, the Central News Agency reported.
In Hong Kong, killing dogs or cats for food is illegal and can be punished by imprisonment of six months and a HK$5,000 fine, though the consumption of the animals is not banned.
But in mainland China, there is no law explicitly banning the eating or sale of dog and cat meat.
An annual dog-eating festival in Yulin, southern China, draws international condemnation every year, with animal rights groups calling for an end to the event.
Last year, American celebrities including Matt Damon and Pamela Anderson called for the festival to be banned. A petition opposing the mass slaughter of dogs received 11 million signatures.
Following the pressure, the Yulin government said it would no longer officially host the festival and that people would not be allowed to slaughter dogs for the festival in public.
The annual event would instead it would be run by commercial businesses and individuals, the government said.