The legal action was filed on Monday in federal court and argues that the rules violate free speech.
The Colorado attorney general’s office is reviewing the suit and declined comment.
State regulations only allow recreational pot shops to advertise in publications believed to have no more than 30 percent of readers under 21. There are no restrictions on medical marijuana advertising.
The lawsuit doesn’t state how the publications might have been hurt by the rule. The latest issue of Westword, Denver’s alternative weekly, has at least nine ads for recreational marijuana businesses.
Opponents previously succeeded in convincing a federal court to overturn a law requiring marijuana publications to be kept behind store counters.