Although Henri had been downgraded from a Category One hurricane, the storm still brought 60mph (95km/h) winds.
Millions of people across Long Island and southern New England have been told to prepare for coastal surges, flooding and downed trees and power lines.
Meanwhile, further south in Tennessee, flash flooding has caused the deaths of at least 21 people.
Dozens of people remain missing in and around the town of Waverly, about 60 miles (90km) west of Nashville, following what local reporters described as unprecedented rainfall.
