Mayor Nutter's press secretary, Mark McDonald, declined to comment, saying, "The city will respond through the legal process."
The NAACP said the city maintained that it could refuse the billboard because of a policy that rejects advocacy or issue advertisements.
Several other airports have also refused to post the NAACP sign for similar reasons.
"But Philadelphia is different, because we found that Philadelphia International had placed other issue-oriented billboards," said Robert Rooks, NAACP national criminal justice director.
In the past, the airport posted ads for the World Wildlife Federation, the national PTA, the USO, and the Center for Missing and Exploited Children, Rooks said.
"The government cannot pick and choose which speech it deems acceptable and which it does not," Chris Hansen, senior staff attorney for the ACLU's Speech, Privacy, and Technology Project, said in a statement.
The billboards are part of an NAACP campaign drawing attention to the relationship between high incarceration rates and poorly performing schools.
The statistics come from a report prepared by the International Centre for Prison Studies at King's College in London. According to the center's most recent World Prison Population List, as of December 2008, the United States incarcerated more people per capita than any other nation, 756 per 100,000 citizens. Russia imprisoned 629; Rwanda, 604; and Cuba, 531.
"That statistic is striking to read and see," Rooks said. "That's why we wanted to elevate it. We want to let people know that this country spends so much on locking people up, when that money would be better used for the education system."
Contact staff writer Sam Wood at 215-854-2796 or samwood@phillynews.com.