The publisher of marijuana magazine High Times has sued the state of Colorado in federal court over the state’s rules preventing recreational cannabis businesses from advertising in most publications.

High Times, along with local weekly magazine Westword, filed the lawsuit on Monday. It marks the first time anyone has challenged the restrictions in court.

The rules allow recreational marijuana businesses to advertise only in publications that are adult-oriented. According to the state’s rules, recreational marijuana stores can advertise only in a publication that “has reliable evidence that no more than 30 percent of the publication’s readership is reasonably expected to be under the age of 21.” There is no such restriction on medical marijuana businesses.

The lawsuit argues the rules, which also restrict television, radio and outdoor advertising, are an unconstitutional restriction of free speech.

The magazines are “chilled from soliciting advertisements from prospective clients and prevented from making revenue from clients who wish to engage in advertising concerning marijuana-related products and services,” the lawsuit’s complaint states.

The lawsuit doesn’t state specific instances in which High Times or Westword were harmed by the rules. In Westword’s latest issue, there are at least nine ads by marijuana businesses advertising that they are open for recreational sales or soon will be.

It is also unclear how the suit’s filing in federal court will impact the judge’s assessment of its claim that the ads concern “lawful activity,” since marijuana is illegal federally.

But publications have previously had success in federal court in overturning another Colorado marijuana law — one that required marijuana-themed publications to be kept behind the counter at stores.

A spokeswoman for the Colorado attorney general’s office said she couldn’t comment because the state’s lawyers hadn’t yet seen the suit.

John Ingold: 303-954-1068, jingold@denverpost.com or twitter.com/john_ingold