Akai Gurley was shot in the chest after he entered the stairwell of his apartment building last month.
The decision comes days after a grand jury opted against charging a New York policeman in the chokehold death of another unarmed black man, Eric Garner.
The decision has sparked protests across the country.
The US was already facing race-related unrest over the decision not to indict a white police officer who had shot dead a young black man, Michael Brown, in Ferguson, Missouri.
In New York City on December, protesters briefly laid down in Macy’s flagship store, at Grand Central Terminal and at an Apple store.
Hundreds streamed along Fifth Avenue and other parts of Manhattan, with banners and chants of “Black lives matter” and “I can’t breathe” – a reference to the words of Eric Garner as he was being restrained by a white police officer.
Protests were also held in other US cities including Chicago, Washington, Denver, and Boston.
Meanwhile, a memorial service was held for 28-year-old Akai Gurley in New York ahead of his funeral on December 6.
At an earlier news conference, his mother tearfully demanded justice for her son.
Speaking alongside her, Kevin Powell, president of the advocacy group BK Nation, called the shooting part of a “series of modern-day lynchings”.
In announcing the grand jury – a body that determines whether to bring criminal charges – Brooklyn’s District Attorney Ken Thompson said it was important to conduct a full and fair investigation.
Police say Akai Gurley and his girlfriend had opened a door into the unlit stairway and an inexperienced officer on a routine patrol fired his gun.
New York Police Commissioner William Bratton called the shooting an accident. However, the medical examiner has ruled that the death is a homicide.
Civil rights leader the Reverend Al Sharpton had initially planned to speak at Akai Gurley’s memorial service but later said he would pay his respects without making an address.
UN human rights experts earlier expressed “legitimate concerns” about grand juries failing to charge the two policemen involved in the deaths of Eric Garner and Michael Brown.
In a statement, UN Special Rapporteur on minority issues, Rita Izsak, said it was part of a broader “pattern of impunity” concerning minority victims.
Following the outcry over the Garner case, New York Mayor Bill de Blasio ordered the city’s 22,000-strong police force to be retrained in how to better communicate and remain calm when making arrests. They will also be fitted with body cameras.
Activists have called for another march in Washington on December 13, followed by a summit on civil rights.
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