The fire on the top floors of an eight-storey building in the rue Erlanger in the wealthy 16th district of southwest Paris is one of the most deadly in the capital in years.
The blaze left around 30 people, including six firefighters, with injuries.
"One person has been arrested. It's a woman. She's currently in custody," Paris prosecutor Remy Heitz said from the scene on Tuesday morning.
French radio station France Info reported that there was a disagreement between neighbours.
The fire started at about 1:00 am local time and was finally brought under control more than five hours later by around 200 firefighters.
Firefighters have yet to search the upper floors of the eight-storey block, where the fire was apparently the most violent and so there are fears that the death toll could increase.
Some of those affected scrambled on to nearby roofs to escape the smoke and flames.
About 50 people were evacuated from the block and two adjacent buildings were also evacuated.
The residential neighbourhood lies on the edge of the vast Bois de Boulogne park and close to the stadium of football club Paris Saint-Germain, the Parc des Princes.