A federal lawsuit filed Wednesday by the National Association for the Advancement of Colored People claims the refusal violates freedom of speech.
The ad reads: "Welcome to America, home to 5 percent of the world's people and 25 percent of the world's prisoners. Let's build a better America together."
The lawsuit says airport officials accept ads from other advocacy groups, including the World Wildlife Federation.
The American Civil Liberties Union is backing the complaint. The defendants are the city, which oversees the airport, and Clear Channel, which handles airport advertising.
Jennifer Burns at the city solicitor's office declined comment on pending litigation. A Clear Channel spokesperson could not immediately be reached.