"Recently participants from an 'open carry' demonstration in Texas brought guns (including military-style assault rifles) into one of our restaurants," Chipotle said in a statement.
Because the incident "created an environment that is potentially intimidating or uncomfortable for many of our customers, we think it is time to make this request," it added.
Anti-gun activists began a "BurritosNotBullets" campaign, after publication of a photo over the weekend which showed people armed with guns in a Chipotle near the city of Dallas.
The chain quickly responded, "respectfully asking that customers not bring guns into our restaurants, unless they are authorized law enforcement personnel."
The activist group behind the campaign, Moms Demand Action for Gun Sense in America, declared victory on Twitter and thanked Chipotle for listening.