Mexico City's prosecutors' office said at least one foreigner was among those injured.
The prosecutors' office said investigators were trying to find those responsible for the attack, but few crimes in Mexico are solved. The victims were identified as three men and two women whose ages ranged from 22 to 46, officials said.
People in Plaza Garibaldi screamed and ran when they heard shots around 10pm on Friday, although some appeared unfazed by the gunfire.
Mexico City has a much lower murder rate than other violence-plagued regions in Mexico where drug cartels battle for control, but the number of murders has surged in the capital since 2014. Mexican authorities say at least four people have been killed and nine wounded in a shooting at the capital's emblematic plaza.
Garibaldi, on the edge of the touristy, colonial historic center of Mexico City, is known for seedy strip clubs and dive bars, aside from mariachis.
Image Debris around Plaza Garibaldi after the shooting
Dozens of people stayed in the area to drink and listen to live music, even after police cordoned off the shooting site and placed yellow markers where bullet casings had fallen.
In footage from the scene, gunshots can be heard over footage of a man playing "La Cucaracha" on a large harp.
Hope said the shooters targeted a specific restaurant on the plaza in what may have been a shakedown for protection money or a hit on rivals.
For the past 12 years, Mexico has fought violent drug gangs by deploying thousands of police, soldiers, and intelligence officers to crack down on cartels and their leaders.
Plaza Garibaldi is located near the notorious Tepito neighbourhood, where a local gang that distributes drugs in the sprawling capital of 21 million is based.
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