It happened on the sixth floor of Third at Bankside, an apartment building on Third Avenue in Mott Haven, just after 10:15 p.m. Wednesday.
The NYPD said they encountered the 24-year-old man who was holding a large machete.
"One of my cops discharged a Taser to try to turn the male from using the machete, and one of the other cops, when the Taser was not successful, fired one round from his 9mm handgun, striking the male in the left arm," said Commanding Officer Benjamin Gurley, NYPD Patrol Borough Bronx.
The officers wrapped a tourniquet around the suspect's arm before he was rushed to Lincoln Hospital in stable condition.
The man has one prior arrest. Police are looking whether he has prior domestic violence incidents.
The two officers assigned to the 40th Precinct were not injured, but taken to the hospital to be checked out.
The shooting is under investigation by the NYPD's Force Investigation Division.
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