Paris police said gunfire had been exchanged and some officers had been wounded.
Unconfirmed reports said Abdelhamid Abaaoud, the alleged mastermind of the attacks, is the focus of the operation.
The so-called Islamic State (IS) group has said it carried out the attacks in which 129 people died.
Roads have been blocked off around Rue de la Republique in Saint Denis, in the same district as the Stade de France, where suicide attackers detonated bombs on Friday.
Radio Monte Carlo reporters at the scene said more than one suspect had been cornered in a block of flats.
Amateur video aired by TV stations BFMTV and iTele cited witnesses saying sporadic gunfire had rung out since around 04:30 local time (03:30 GMT).
Deputy Mayor Stephane Peu urged local residents to stay indoors, saying "it is not a new attack but a police intervention".
Friday's attacks also left more than 400 people wounded, with 221 still in hospital, 57 of them in intensive care.
(BBC News)