Mexico City's prosecutors' office said at least one foreigner was among those injured.
The armed men opened fire at a road crossing on the edge of the Plaza Garibaldi, a major tourist attraction packed with mariachi bars, police said. 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. No arrests have been made.
The identity of the three dead was not immediately clear, but the Milenio newspaper said they were men.
The historic site is also blocks from one of Latin America's largest public squares, where thousands will flock on Saturday night to see President Enrique Pena Nieto deliver the traditional cry of "Long Live Mexico!" to celebrate Independence Day.
Mexican news outlet La Silla Rota circulated surveillance video of the alleged assailants wearing traditional embroidered jackets and trousers as they fled on motorcycles. Mariachi musicians returned to the square around the same time the shooting took place a day prior.
Investigators later found 60 empty bullet casings on the ground. A video posted to social media showed a musician at a colourful Plaza Garibaldi restaurant strumming Mexican tune "La Cucaracha" on a harp without pausing as multiple shots loudly ring out nearby. The city - known to be a popular tourist destination for those looking to experience arts, food and culture - has relatively stayed out of the drug violence plaguing other tourist hotspots, Reuters reported.
In 2013, United States civil rights leader Malcolm X's grandson, Malcolm Shabazz, was beaten to death near the square after a dispute over a nightclub bill.
Plaza Garibaldi borders one of Mexico City's most notorious neighborhoods, Tepito, home to La Union gang, which police say is behind a spurt in drug-dealing and protection rackets.