The woman, who climbed to the feet of the statue to protest the separation of migrant families, is in detention, police said.
The protest came hours after several other demonstrators had hung a banner on the statue’s pedestal and had been arrested.
The climber – named by a federal official as Therese Okoumou – engaged in a four-hour standoff with police before two officers climbed up to the base and went over to her.
With the dramatic scene unfolding on live television, she and the officers edged carefully around the rim of the statue’s robes toward a ladder, and she climbed down about eight metres to the monument’s observation point and was taken into custody.
The woman had participated earlier in displaying a banner calling for abolishing the federal government’s chief immigration enforcement agency, said Jay W. Walker, an organiser with Rise and Resist, which arranged the demonstration.
The group initially tweeted that the climber had ‘no connection’ to the demonstration.
Mr Walker later said she was involved but others had no idea she would make the climb, which was not part of the planned protest.
He said: ‘We don’t know whether she had this planned before she ever got to Liberty Island or whether it was a spur-of-the-moment decision.’
Regardless, he said he felt the publicity would help the group’s cause.
A spokesman for the National Park Service, which runs the monument, saw it differently.
Spokesman Jerry Willis said: ‘I feel really sorry for those visitors today who had to leave or couldn’t come.
‘People have the right to speak out. I don’t think they have the right to co-opt the Statue of Liberty to do it.’
He added that visitors were forced to leave Liberty Island hours before its normal 6.15 pm closing time.
Earlier and farther below, at least six people were taken into custody after unfurling a banner that read ‘Abolish I.C.E.,’ referring to US Immigration and Customs Enforcement, whose officers arrest and deport immigrants who are in the US illegally, among other duties.
Mr Willis said federal regulations prohibit hanging banners from the monument.
Rise and Resist opposes US president Donald Trump’s administration and advocates ending deportations and family separations at the US-Mexico border.
Under Mr Trump’s zero-tolerance policy, the government has begun requiring border agents to arrest and prosecute anyone caught entering the country illegally.
That resulted in more than 2,000 children being separated from their parents within six weeks this spring.
Under public pressure, Mr Trump later halted his policy of taking children from their detained parents.
A federal judge in California ordered the Trump administration late last month to reunite the more than 2,000 children with their parents in 30 days.
The Statue of Liberty has long been a welcoming symbol for immigrants and refugees coming to the US. It also has been a setting for protests and other activities that forced evacuations.