The officer was the fourth killed in the line of duty in the past 11 months, police commissioner William Bratton told a news conference.
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He named the slain officer as Randolph Holder, 33, a Guyanese immigrant who had been on the force for five years.
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A suspect has been arrested, the commissioner added.
Holder and other officers were responding to reports of gunfire in the Harlem area of the city when they confronted a man riding a bicycle, the Times said, quoting a police officer.
A bystander had told police his bicycle had been stolen at gunpoint.
"He ran toward danger," Bratton said. "It was the last time he will respond to that call."
Holder's father and grandfather worked as police officers in Guyana on the northern coast of South America.
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