Facebook is expected to hold its initial public offering next month. The company filed the required paperwork with the U.S. Securities and Exchange Commission in January. The SEC requires public companies to disclose the diversity of their boards.

About 11 percent of Fortune 500 companies had all-male boards in 2011, according to a study by Catalyst. Facebook's user base is nearly 60 percent female. But the company has a prominent top female executive in Sheryl Sandberg, its chief operating officer.

"Facebook and many other Silicon Valley tech companies are predominantly populated by males and male engineering culture," said Ray Valdes, an analyst with Gartner. "However, Facebook is a bit different in that they have a very strong female at the helm or near the helm."

Valdes said Sandberg's prominence would likely prevent the Ultraviolet petition from gaining "huge traction."

Susan Herring, a professor at Indiana University who has studied gender and communications, said that, because more than half of Facebook's users are female, more than half of its board should "ideally" be women. But, she said, "The actual situation reflects historical factors," including the scarcity of women in computer science.