The Statue of Liberty itself received little or no damage. The pedestal and base, including the main floor and exhibits upstairs, are OK. But docks, a brick promenade, railings and other facilities on Liberty Island were damaged.
At Ellis Island, the storm damaged doors, windows and exhibits in the ferry building among other sites.
Park Service spokeswoman Daphne Yun said no projected reopening date has been established.
Both the statue and Ellis Island, which served as an entry point for immigrants for a half-century, are among New York's top tourist attractions.