"You made a huge mistake by taking one of us. Release him. And if anything happens to him, you (expletive) will always remember this upcoming November 5th," the group says in a Spanish-language YouTube video that shows buildings being blown up.
November 5 is commonly referred to as Guy Fawkes day in honor of the Brit who tried to blow up parliament in the Gunpowder Plot of 1604. Fawkes was immortalized in the 2006 movie "V For Vendetta" about a freedom fighter who uses terrorist tactics against a totalitarian society.
"We demand his release," says a man wearing a suit and tie and the mask from "V for Vendetta" that has become the symbol for Anonymous. "We want the Army and the Navy to know that we are fed up with the criminal group Zetas, who have concentrated on kidnapping, stealing and blackmailing in different ways."
The video, posted earlier this month, also threatens to expose journalists, taxi drivers, and police who allegedly cooperate with the cartel.
"We can't defend ourselves with a weapon, but if we can do this with their cars, houses, bars, brothels, and everything else in their possession," the video says. "It won't be difficult. We all know who they are and where they are."
The man in the video uses an accent from Spain and Mexican slang, according to the Houston Chronicle.
The video does not identify the missing member of its group, but says he was kidnapped while he was "doing Paperstorm," which is a reference to posting flyers and other printed messages in public spaces.
It's a gutsy move for Anonymous, which typically targets corporations, government agencies, and law enforcement departments that it deems morally and financially corrupt. The U.S. Justice Department says the Zetas cartel "may be the most technologically advanced, sophisticated, and violent" of the paramilitary enforcement groups in Mexico.
Elinor Mills covers Internet security and privacy. She joined CNET News in 2005 after working as a foreign correspondent for Reuters in Portugal and writing for The Industry Standard, the IDG News Service, and the Associated Press.