The statue was not damaged by superstorm Sandy, but Liberty Island sustained significant infrastructure damage that will delay the monument's re-opening indefinitely, said Mark Litterst, a Park Service spokesman.
"It was quite a shock to see the extent of the damage,'' Litterst said.
Officials said Ellis Island's invaluable cache of historical documents and records was not harmed by the storm.
Power was restored to Liberty Island on Saturday night, but its main administration building, which houses the park's mechanical systems, sustained severe damage from four feet (1.2 metres) of flood water, Litterst said.
Liberty Island's dock, where tourists arrive by ferry from Manhattan's Battery Park and New Jersey's Liberty State Park, also sustained significant damage and may need to be rebuilt.
"The walkway just got lifted off the pilings and shifted off its support," Litterst said. "We may be able to repair the dock if it's still structurally sound, but if not it will have to be replaced, and that's a longer process."
The 305-foot (93-metre) monument, which the park service says can sway up to 3 inches (7.6 cm) in winds of 50 mph (80 kph), was closed to visitors for a year during an extensive renovation. It had only been open for six hours last month when Sandy roared into New York Harbor.
More than 300 members of the National Park Service's incident response team are assessing damage to 15 national parks sites in Sandy's path.
"When asked to respond to a place like the Statue of Liberty, we drop everything and go," said Litterst. "We're as anxious as anybody to find out how long it will take to get it fixed up and open its doors again to the American public."