The suggestion comes as the chicken chain announced plans to open a restaurant in Queens Center Mall, the fourth location in the city.
"We look forward to opening our first restaurant in Queens and serving all of our customers delicious food in an environment of genuine hospitality," a Chick-fil-A spokesperson said.
But de Blasio says Chick fil-A supports groups that promote discrimination against gay people.
"What the ownership of Chick-fil-A has said is wrong," de Blasio said. "I’m certainly not going to patronize them, and I wouldn’t urge any other New Yorker to patronize them. But they do have a legal right."
"Chick-fil-A is anti-LGBT," councilman Danny Dromm said in a statement. "This group imparts a strong anti-LGBT message by forcing their employees and volunteers to adhere to a policy that prohibits same-sex love. It is outrageous that Chick-fil-A is quietly spreading its message of hate by funding these types of organizations."
In 2012, Chick-fil-A gained attention when it came to light that the company had donated millions of dollars to organizations that fight same-sex marriage.
The restaurant chain, which is closed on Sundays, is known for heralding Christian beliefs.
"As it relates to society in general, I think we are inviting God’s judgment on our nation when we shake our fist at him and say, ‘We know better than you as to what constitutes a marriage,'" Dan T. Cathy, the company’s president and chief operating officer, said in an interview.
But a Chick-fil-A spokesperson said that the company employees thousands of people who represent varied backgrounds and beliefs and that the business' main focus is on satisfactory service and food.
"The Chick-fil-A culture and service tradition in our restaurants is to treat every person with honor, dignity and respect -- regardless of their beliefs, race, creed, sexual orientation or gender," the spokesperson said.