Dennis Herrera filed a motion for dismissal Thursday, the San Francisco Examiner reported.
"Public-nudity bans are a longstanding feature of municipal codes throughout the nation, and their constitutionality has been repeatedly affirmed by the courts -- including the U.S. Supreme Court," Herrera said in a statement.
The law is scheduled to take effect Feb. 1. It was sponsored by Scott Wiener, a city supervisor who represents the Castro district, one of the country's best-known gay neighborhoods.
While nudity in the Castro, especially in Jane Warner Plaza, has a long history, Wiener says many of his constituents, including business owners, are sick of it. The law requires genitals and rear ends to be covered, although naked breasts are still allowed.
Opponents of the law argue it also violates the Equal Protection clause because nudity would still be allowed during a few special events. Herrera said that could lead to a broader ban with everyone required to be clothed even during the Folsom Street Fair.