The shooters injured a further eight people as they opened fire at a busy tourist area of the Plaza Garibaldi.
The area, home to notoriously violent drug gangs, was busy with locals celebrating the weekend's Independence Day.
Cops said the gunmen fled the scene on motorbikes.
The Mexico City prosecutors' office said at least one foreigner was among those wounded in Friday night's attack.
Local media said the attack was staged by three gunmen.
Four people died initially and a fifth died of her wounds at a hospital Saturday afternoon, authorities said.
The news outlet La Silla Rota circulated surveillance video of the alleged assailants wearing traditional embroidered jackets and pants as they fled on motorcycles.
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 Sept. 16, 1810.
Lisa Sanchez, director of Mexicans United Against Delinquency, described the shooting as a "piercing portrait" of Mexico.
The prosecutors' office said investigators were trying to find those responsible for the attack.
A Mexican security expert, Alejandro Hope, said the Friday shooting appeared to be a hit by an organised crime group.
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