More than 100 firefighters battled the blaze in the 18th district of the French capital, at the foot of the Montmartre hill and its tourist attractions.
The fire - the deadliest in Paris since 2005 - quickly became a criminal investigation after it emerged it had broken out in two separate places in the building.
Police arrested a man in his 30s "who might have been at the scene" of the fire, a source at the Paris prosecutor's office said, although he stressed the investigation was at an early stage.
Tissem Ferjani, a pastry chef who lives on the same road, said she had seen "lifeless bodies on the ground" after residents had jumped in a desperate effort to escape the raging flames.
"I was woken up around 4:00 am by people screaming for help. They had no choice - either they stayed where they were and died or they got out through the window and they fell.
"Everyone in the district came out to try to help them."
Interior Minister Bernard Cazeneuve told Europe 1 radio that the authorities were "focusing on the possibility of criminal intent".
Firefighters were first called to the scene at 2:20 AM local time and quickly put out the blaze, but they were called back again two hours later to extinguish a second, much larger fire.
The blaze started on the ground floor of the five-storey building before spreading into the stairwell.
The eight victims included two who died after they attempted to escape through windows, according to police. A source close to the investigation said two children were among the victims.
It had been recently renovated and was equipped with an entry code system.
The mayor said 15 buildings in the district had been affected by the inferno.