Streets and work places near to the explosion - which occurred in the sixth arrondissement, thought to be on the rue Bonapart - have been evacuated.
Other buildings nearby were also damaged.
In total 17 people were injured in the blast, which went off at around 12:30pm local time (11:30am UK time).
According to French paper Liberation, a firefighter was seriously injured; the other injuries were less severe.
Images posted online showed the residential building in flames and smoke rising above the Paris skyline.
Police have confirmed the blast was caused by a domestic gas leak, and is not an attack, local media is reporting.
However witnesses told local media of their fears that the blast had been caused by a bomb, with memories of the attacks which left 130 dead in November, and last week's attacks in Brussels, still fresh.