Police arrested 19-year-old Michael Wayman in connection with the shooting on Thursday night.
Two people are being treated, and police are talking to suspects.
The incident happened around 7 p.m. Wednesday at Bronx Lebanon Hospital.
Police say two men, a nurse and a security guard, are being treated for non-life threatening injuries.
Hospital administrators say it's the first time such an incident has occurred on the property. The building does not have metal detectors, and most guards are not armed. However, officials say the staff is trained to deal with all kinds of situations.
"It's completely unusual," hospital spokesman Errol Schneer said. "We have never had a situation such as this ever happen or occur. But we are fortunate that we have a trained security force that's able to address the situation very quickly."
Investigators say the shooting was the continuation of an argument that started earlier in the day and is likely gang related.
Wayman is being charged with 1st Degree Assault and Criminal Possession of a Weapon.