The FDNY vehicle apparently had its lights on and collided with the van at Burgher Avenue and Richmond Road just before 12:15 p.m.
The force of the crash spun the van around and sent it careening onto the sidewalk.
A witness told the Staten Island Advance that the fire truck, from Ladder 81, had its siren on as it traveled down Richmond Road, toward the Staten Island Expressway.
The witness, Ali Alsaede, said the van turned left onto Richmond Road and the fire truck hit the van's rear driver-side door.
Nine people from the van were taken to a hospital, including the three critically injured. One person later died.
Six firefighters suffered minor injuries.
The FDNY vehicle, Ladder 81, was responding to a car fire at the time of the crash.