Authorities say the suspect, Malik Facey, assaulted the captain just before 2:30 p.m. at the George R. Vierno Center.
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Facey was taken into custody, and the department is pursuing additional charges.
He was being held at Rikers Island in connection with a July 2019 shooting.
"This was a heinous assault on a captain who was just doing his job," Department of Correction Commissioner Louis Molina said. "Violence against staff is never tolerated. Assaults in jail are as much a crime as assaults on the street, and we are pursuing re-arrest and supporting charges against the individual responsible. We have zero tolerance for assaults on staff."
The weapon used in the attack was recovered, officials said.
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The officer was treated at a local hospital, where he remains in stable condition.
The incident is currently under investigation.
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