Last Updated Dec 1, 2015 1:40 PM EST
The first-of-its-kind rule will require a salt-shaker emblem on some sandwiches, salads and other menu items that top the recommended daily limit of 2,300 milligrams - about a teaspoon - of sodium.
It's the latest in a series of novel nutritional moves by the nation's biggest city, and it comes as health advocates, federal regulators and some in the food industry are trying to get Americans to cut down on salt. Experts say most Americans consume too much of it, raising their risks of high blood pressure and heart problems.
"When you see this warning label, you know that that item has more than the total amount of sodium that you should consume in a single day," city Health Commissioner Dr. Mary Bassett said Monday at an Applebee's in Times Square, as 40 of the chain's New York City-area locations announced they had added the labels ahead of the deadline.
The average American consumes about 3,400 mg of salt per day, and public health advocates have cheered the measure as a smart step to make diners aware of how much sodium they're ordering. A T.G.I. Friday's New York cheddar and bacon burger counts 4,280 mg, for example; a Chili's boneless Buffalo chicken salad has 3,460 mg. The figures come from the companies' published nutritional information.
"I think this is another important initiative along with the calorie labeling rule," said Rebecca Blake, senior director of clinical nutrition at Mount Sinai Beth Israel in New York. "But we must remember to provide the consumers with adequate education on how to reduce sodium intake and where to find hidden salt in our diets - it certainly is not limited to fast food."
A great deal of the sodium Americans eat is incorporated into prepared foods, not added from a salt shaker, so people often don't have a good sense of how much they're consuming over the course of a day.
"I think one of the things the salt labeling will do is point out to people how much salt is in food that they may not be aware of. For instance, whole wheat bread can have more salt than a bag of potato chips," Dr. Jonathan Newman, a cardiologist and assistant professor of medicine at NYU Langone Medical Center, told CBS News.
"With salt, [labeling] is particularly important because 75 percent of the salt we take in as Americans is essentially hidden," CBS News medical contributor Dr. Holly Phillips said on "CBS This Morning" in September. "It's in restaurant food, it's in processed food that may not even taste salty. Only 10 percent of the salt we get comes from the salt shaker."
Partly due to all this "hidden" salt, "the average American eats two to three times the recommended daily intake of salt a day, which we know is very tightly linked to the development of high blood pressure, a very important cause of stroke and heart disease," Newman said.
But salt producers say the city is acting on false impressions about the risks of salt in New Yorkers' diets. An international study involving 100,000 people suggested last year that most people's salt intake was OK for heart health, though other scientists faulted the study.
Restaurateurs say healthy eating initiatives shouldn't single out any one ingredient and that the city shouldn't create its own salt-warning scheme when federal regulators are working on new, national sodium guidelines.
"Every one of these cumbersome new laws makes it tougher and tougher for restaurants to find success," New York State Restaurant Association President Melissa Fleischut said when the city health board approved the salt requirement.
It will apply to an estimated 10 percent of menu items at the New York City outlets of chains with at least 15 outlets nationwide, according to the Health Department. Officials say those chains do about one-third of the city's restaurant business.
While eateries are expected to comply as of Tuesday, the city won't start collecting fines until March 1.
In recent years, New York City has pioneered banning trans fats from restaurant meals and forcing chain eateries to post calorie counts on menus. It led development of voluntary salt-reduction targets for various table staples and tried, unsuccessfully, to limit the size of some sugary drinks.