The lawsuit filed in federal court on Monday claims the rules violate free speech, The Denver Post reported.
State regulations only allow the shops to advertise in publications that have “reliable evidence that no more than 30 percent of the publication’s readership is reasonably expected to be under the age of 21.”
Carolyn Tyler, a spokeswoman for Colorado Attorney General John Suthers, said Wednesday that lawyers were reviewing the suit and couldn’t comment.
There are no restrictions on advertising for medical marijuana.
Washington, where recreational pot is also legal, also bars marijuana advertising aimed at minors.
The lawsuit doesn’t give specifics about how the publications might have been hurt by Colorado’s restrictions.
The latest issue of Westword has at least nine ads for recreational marijuana businesses.
The lawsuit claims the publications are “chilled” from soliciting ads from prospective clients and prevented from making revenue from those that wish to advertise about pot-related products and services.
Opponents previously succeeded in convincing a federal court to overturn a law requiring marijuana publications to be kept behind store counters.