Hanoi's vice mayor Nguyen Van Suu also said that slaughtering dogs and cats for their meat was disturbing to foreigners and would "negatively impact the image of a civilized and modern capital."
His message was published on the city's website.
Suu also instructed local governments to raise awareness of the risk of rabies when consuming dog and cat meat.
His move is part of an effort to stamp out rabies in Vietnam by 2021. The move is a contentious one as many Vietnamese believe that eating dog meat increases stamina and the dish is thought of as a delicacy.
There are 493,000 dogs and cats in Hanoi, of which 10% are raised for commercial purposes, including for their meat.
"People eat dog meat and there's no problem," said Nguyen Thi Minh, the owner of a dog meat restaurant in Hanoi.
"I serve customers from South Korea, the United States and other countries."
She added that her restaurant cooked dog meat properly so there was no risk of rabies.
Associated Press contributed to this report.
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