NEW YORK — New York on Thursday became the first city in the nation to ban super-sized sugary drinks in restaurants, setting the stage for a legal challenge by the beverage industry, which calls the rule a violation of consumers’ rights to drink what they want even if it is destroying their health.

The Board of Health, which is appointed by Mayor Michael Bloomberg, easily approved the rule, which will limit to 16 ounces the size of sodas and other sugary drinks sold in food-service establishments such as restaurants and delis.

Assuming it is not blocked by legal challenges, it would take effect in six months and impose a $200 fine on businesses found in violation.