Local media reported that the people were in the buildings of the American Civic Association (ACA) in the Binghamton, north of New York City.
Mayor Matthew Ryan told reporters the man had a high-powered rifle and was still believed to be in the building.
Unconfirmed local media reports said up to 13 people may have been killed in the incident.
Television footage showed four people being carried from the scene on stretchers. Their condition was not known.
The Binghamton Press & Sun Bulletin said homes nearby were being evacuated and a police commando unit was at the scene.
It said apartments and a nearby school and care home were under lockdown and some streets had been sealed off.
Eyewitness reported seeing a man of Asian appearance in his 20s entering the building.
A spokeswoman at a local hospital said at least one person was being treated for unspecified injuries.
"We're on full alert anticipating we're going to get additional casualties," Linda Miller said.
Reports said people had been hiding in the basement of the building and inside a storage room.
The ACA says on its website that it assists immigrants and refugees with personal and immigration counselling.
