The measure is designed to protect the city's poor as more retail stores refuse to take cash from shoppers and only accept debit card and credit card payments.
Fines of up to $1,500 would be levied against businesses that violate the proposed law.
Mayor Bill de Blasio has indicated he supports the bill but first wants it to undergo a review process.
Stores would also be prohibited from charging customers higher prices for paying in cash but would still be able to refuse bills above $20.
They would also be able to ban cash for transactions that take place online, by phone or mail.
If signed by the mayor, the cashless ban would take effect in nine months.
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