Firefighters say the woman, identified as 25-year-old Lashanda Armstrong, had just been involved in a domestic dispute.
Authorities said a 10-year-old boy was able to clamber out the window of the minivan. The boy's siblings - two boys, ages 5 and 2, and an 11-month-old girl - were not able to escape.
When the van hit the water at about 8 p.m., it was just past high tide and the Hudson was flowing swiftly to the south, pulling the van some 25 yards out into the rain- and melt-swollen river, fire chief Michael Vatter said. Vatter figured the van floated in the 45-degree water for no more than two minutes.
"He got out of the car, got up onto the boat ramp, turned around and it was gone," Vatter said.
The boy ran to a nearby fire station and alerted firefighters, Vatter said.
Divers recovered the bodies of the mother and her three young children about an hour later.
Police said there was no history of domestic violence at the address.
Newburgh, which has about 30,000 residents, sits on the western shore of the part of the river that runs south through New York state and eventually splits New York and New Jersey.
A similar incident occurred in 2006, about 20 miles south of Newburgh.
The Associated Press contributed to this story.