Sources said the suspects were shot by police, as Reuters news agency reported that a female suspect killed herself by detonating a vest rigged with explosives.
The identity of the casualties was not immediately released. However, French media said the target of the operation was Belgian national Abdelhamid Abaaoud, a key suspect of Friday's attacks, in which at least 129 people were killed.
Another suspect, Salah Abdeslam, was also said to be a target in the raids.
Police said some of the suspects were holed up in an apartment in the suburb early on Wednesday. Three police officers were wounded in an initial shootout, Bloom Gist learnt from sources.
Residents of the area in northern Paris first reported hearing bursts of gunfire at 4:30am (3:30 GMT), as police exchanged fire with one or more suspects.
After a short lull in the operation, at least seven explosions were heard at 6:30 GMT.
Heavily armed special police units and ambulances were gathering at the scene as a helicopter was hovering over the area, reports said.
Police were telling onlookers to clear the vicinity of the operation and blocked off a street in the area, as ambulances and fire engines lined the streets a stone's throw from the centre of Saint-Denis.
French President Francois Hollande on Wednesday will hold a meeting to discuss proposals to extend by three months the state of emergency declared after the worst attacks in French history.
It will then be put to vote by lawmakers on Thursday and Friday.
