The five gunmen, dressed as mariachi musicians, were armed with rifles and handguns as they opened fire on Plaza Garibaldi, an attack that also injured at least nine others including a foreign national.
The former Mexico City mayor, who takes office December 1, has vowed that new strategies under the city's incoming mayor, Claudia Sheinbaum, will be effective.
In a statement, police said the victims died close to Plaza Garibaldi, a major tourist destination packed with mariachi bars. Many Mexicans will wear mariachi costumes, a symbol of national pride, on Saturday night to commemorate the launch of the revolt against Spanish rule on September 16, 1810.
The prosecutors' office said investigators were trying to find those responsible for the attack, but few crimes in Mexico are solved.
Curious onlookers gather on the perimeters of a crime scene after a shooting in Garibaldi Plaza in Mexico City, Friday, Sept. 14, 2018.
The shooting took place as crowds kicked off Mexico's Independence Day celebrations on Friday and during a busy night at Plaza Garibaldi, a popular square where mariachis play around the clock for tourists and locals. 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.
Another 37,000 people are reported as missing.
Mexico City has experienced less of the drug violence that plagues cartel strongholds in other regions of the country.
Police blame much of the capital's crime on retail drug dealing and protection rackets run by violent gangs.
Officials in the Mexican capital have blamed the rise in crime on drug dealing and protection rackets, while the government claims that at least one of the city's violent gangs is connected to the Jalisco New Generation Cartel.