More than 80 people died in Monday's storm, which brought destruction to the east coast of the United States.
More than 47,000 people were due at the start line at Staten Island on Sunday but it is not clear how many will now be able to attend.
Race organizer Mary Wittenberg said staging the marathon would show the "vitality and spirit" of New York City.
Opening hours for runners to pick up their race numbers and kit have been extended.
New York Road Runners, who are organizing the event, have issued an appeal for additional volunteers to help out. "We're adjusting Marathon Day plans as a result of the storm's impact on our operations and resources," a spokesperson said.
"At every turn, we will be working to ensure that our planning doesn't affect any recovery efforts."
The opening ceremony, which had been set to include a parade of nations in Central Park along with a spectacular fireworks display, has been cancelled, as has a 5km dash to the finish line that would have run through Midtown on Saturday.
