The officer is the second Department of Correction employee to test positive for the virus. David Perez, who works for the Investigation Division, died on Monday.
The second officer has not been identified.
The NYC Correction Officers' Benevolent Association held a news conference Wednesday to plead for more supplies to protect them from the virus.
The union said they need better masks, more wipes and cleaners to protect themselves.
New York City's Board of Correction this week called for the immediate release of all high-risk inmates after the investigator's death. Perez, 56, was said to have a pre-existing health condition and only limited contact with inmates.
The city's jail system has about 8,000 inmates, most at notorious Rikers Island.
There were 923 confirmed cases of coronavirus and 10 deaths in New York City as of Wednesday morning.
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The Associated Press contributed to this report.