The New York Police Department arrests thousands and thousands of people each year for possessing small amounts of marijuana. That will change next week, when officers will issue a ticket rather than arresting someone with a small amount of marijuana, city officials announced Monday.

Police officers will still arrest someone under certain circumstances, including if the person has a warrant for their arrest, but Mayor Bill de Blasio’s office said that the policy would mean that possessing small amounts of marijuana would only result in a fine.

This change, which begins on Nov. 19, would have a very real impact on the people who are arrested, a group that is overwhelmingly young and black or Latino, according to a recent study from the Drug Policy Alliance and Marijuana Arrest Research Project.

Between January and August of this year, 86 percent of the people arrested for possessing marijuana were black or Latino, while just 10 percent of those arrested were white, the study found. The majority of these people were young adults (more than half were age 25 or younger) and had no real criminal record.

Police in New York still make a sizable number of these arrests each year, even though the overall total has declined in recent years. The number of arrests dipped to 28,000 last year from 50,000 during the later years of the Bloomberg administration, as documented by the Marijuana Arrest Research Project. An analysis by the New York Civil Liberties Union last year called New York City “the nation’s marijuana arrest capital” (and also noted “consistently large racial disparities in marijuana arrests” across the state between 2001 and 2010).

Other New York officials have publicly vowed to move away from focusing so much attention on such arrests. In July, Kenneth P. Thompson, the Brooklyn district attorney, announced that his office would no longer prosecute most cases involving someone found with a small amount of marijuana.

“This new policy is a reasonable response to the thousands of low-level marijuana arrests that weigh down the criminal justice system, require significant resources that could be redirected to more serious crimes and take an unnecessary toll on offenders,” Thompson said in a statement. (In response, William J. Bratton, the New York City police commissioner, said the new policy would not change anything for officers.)

A shift in New York would follow consistent criticism of how the police department treats minority residents, something that has come up again and again in the last mayoral race, discussions of “stop and frisk” and the July death of Eric Garner, a Staten Island man who died after being placed in a chokehold by a city police officer.

This change would have a broader meaning, though, happening in such a high-profile place that is home to the country’s largest police department. And while the focus may be on what this means for how police officers interact with residents — and the way this affects some people much more than others — it also arrives as public opinion on marijuana is clearly trending in one particular direction.

Proponents of legalizing marijuana, fresh off a trio of victories last week, are hoping to get similar ballot measures ready in at least five other states. And a Pew Research Center poll earlier this year, which found that public support for legalizing marijuana had reached an all-time high, also found that even more people agreed that anyone convicted of possessing small amounts of marijuana shouldn’t go to jail:

A year earlier, a broad majority told Pew that enforcing marijuana laws cost more than it was worth. Meanwhile, the share of arrests related to possessing marijuana has significantly increased in recent years. In 2012, for example, one of every eight arrests in New York was for possessing marijuana. In addition to being unpopular, this kind of policing is not cheap.

[This post has been updated now that the policy has officially been announced. The New York Times first reported that the possible shift was looming.]