Five people were killed and several others were wounded, the city's prosecutor's office said.
In a statement, police said the victims died close to Plaza Garibaldi, a major tourist destination packed with mariachi bars. It's unclear whether the shooting was motivated by gang violence, but the Times notes that a district infested with drugs and gangs lies about a mile away.
The number of killings in the city, the Mexican capital, has surged since 2014.
Local authorities said it was unclear why the men opened fire.
The shootings happened just as the Mexican capital was kicking off independence day weekend celebrations.
The news outlet La Silla Rota circulated surveillance video of the alleged assailants wearing traditional embroidered jackets and trousers as they fled on motorcycles.
The prosecutors' office said investigators were trying to find those responsible for the attack, but few crimes in Mexico are solved.
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The roots of mariachi music in Mexico City can be traced to a bar that dominates one side of the plaza.
In one video, a man plucking a large harp continues to belt out the Mexican civil war anthem "La Cucaracha" as dozens of gunshots can be heard in the background, though it isn't clear the musicians heard them.
Videos circulating on social media showed musicians playing music during and after the shooting.
Police blame much of the capital's crime on retail drug dealing and protection rackets run by violent gangs, though the government says at least one of these has links to a major national trafficking group, the Jalisco New Generation Cartel.
Tepito has suffered a wave of violence over August after the gang's presumed leader, Roberto Moyado Esparza or El Betito was arrested.
In 2013, US civil rights leader Malcolm X's grandson, Malcolm Shabazz, was beaten to death near the square after a dispute over a nightclub bill.