There have been other attempts in Mexico to ban the ballads known as "narcocorridos," but seldom have they affected a mainstream group as popular as Los Tigres.
The band has been a mainstay of norteno music for decades, with hits like "Contrabando y Traicion" (Contraband and Betrayal) and "Jefe de Jefes" (Boss of Bosses).
"The musical group will not get permits for future shows in the city limits, until such time as authorities decide otherwise," the city said in a statement.
The Chihuahua city government said the band violated a three-month-old city ordinance prohibiting songs that glorify traffickers, and that the concert's organizers would be fined "at least 20,000 pesos" ($1,585).
The band appeared Saturday at a concert organized as part of a cattle expo.
A Twitter posting on an account linked to the band's official website claimed the group was surprised at the ban and was not aware of the ordinance.
The posting said the band had played "La Reyna del Sur," (The Queen of the South), a song believed to refer to alleged female drug capos like Sandra Avila Beltran, better known as the Queen of the Pacific.
City Governance Director Javier Torres Cardona said "we ask concert organizers and the artists themselves to think about the difficult situation the country is in."
According to official figures, drug-related violence has cost the lives of at least 47,515 people in Mexico from December 2006 through September 2011.
Chihuahua state, which lies on the U.S. border and contains Ciudad Juarez along with Chihuahua city, has been particularly hard hit by drug cartel violence.
On Monday, gunmen burst into a barber shop in Chihuahua and shot to death five young men, including one who was getting a haircut at the time, city officials said.
It is not the first time the Tigres del Norte have had run-ins over controversial songs.
The group canceled a planned appearance at an awards ceremony in 2009 after organizers allegedly asked it not to play the song "La Granja" (The Farm). The song's biting lyrics appear to lampoon former officials and also allude to the violence unleashed in Mexico's war on drug cartels.
Since 2002, here have been several scattered attempts by local governments in Mexico to ban narcocorridos, which are a subgenre that updates Mexico's folkloric "corrido" tradition of singing about revolutionary heroes to tell the story of, and sometimes lionize, drug traffickers.
In 2011, Sinaloa state implemented rules to rescind the liquor licenses of businesses that play the songs.