More than 200 firefighters battled the blaze, which broke out around 1 am local time (0500 GMT), a spokesman for the New York Fire Department told AFP.
The injured include 23 firefighters and 11 civilians whose conditions "range from minor to serious," the spokesman said.
It was not immediately clear what caused the inferno, which appeared to have started in a townhouse and spread to two others.
The NYFD spokesman said firefighters were close to getting the blaze under control.
Staten Island is one of New York City's five boroughs.
