The blast, which occurred at a bakery at 9 a.m. local time on Saturday, killed two firefighters who were responding reports of the leak, while a Spanish national died hours after the incident in hospital.
"Profound sadness. Standing by the families of victims. The nation shares in their pain," French Interior Minister Christophe Castaner tweeted after the explosion, adding that 10 people, including a firefighter, were seriously injured and a further 37 were "in a state of relative emergency."
Pictures from the scene, on Rue de Trevise in the 9th arrondissement of the French capital, showed smashed windows and scattered debris across the street, as fire crews evacuated people from apartments above the bakery.
"At this stage, we can tell the origin of the explosion is accidental, a gas leak, but we should remain prudent as an ongoing investigation will determine the causes of this," Heitz said.
Castaner, who visited the scene with Prime Minister Edouarde Philippe and the city's mayor Anne Hidalgo, wrote earlier on Twitter that the toll of victims "will be heavy."
More than 200 firefighters were responding to the incident, Castaner wrote. "My first thoughts go to those injured and their loved ones," he added.
Police had earlier advised the public to stay away from the area, and to make space for emergency vehicles.
CNN's Saskya Vandoorne and Arnaud Siad contributed to this report.