A French policewoman is among the four taken into custody, French national police said.
The policewoman worked at the Fort de Rosny-sous-Bois, northeast of Paris, the spokesman said.
According to Le Figaro newspaper
, the Fort de Rosny-sous-Bois is the location of an important intelligence center.
Coulibaly killed four hostages in the grocery store before police shot and killed him.
His attack followed one on the office of the French satirical magazine Charlie Hebdo.
France has been under a heightened state of alert since January's terror attacks in Paris that killed 17 people.
Brothers Cherif and Said Kouachi, authors of the deadly attack on the Charlie Hebdo offices, were killed days later after two violent standoffs. The brothers were accused of killing 12 people in a massacre at the magazine offices.
Coulibaly, suspected in the slaying of a police officer, was killed by security forces after he shot and killed four hostages during the siege at the kosher market.
Charlie Hebdo has a controversial history of depicting the Prophet Mohammed, often in an unfavorable light, which has angered many Muslims around the world.
Earlier cartoons depicting Mohammed spurred protests and the burning of the magazine's office three years ago.
Since the attack, European nations have carried out raids on suspected terror cells with links to ISIS in Syria.