French media say DNA traces picked up off the tape used to tie up the reality TV star in a Paris apartment in October led police to the suspects.
According to French broadcaster LCI, the alleged burglars include “old figures of the French mob and organised crime”.
Those picked up in the series of early morning raids across France include “many in their fifties and even a 72-year-old man”.
Kardashian was robbed of around €10m (£7m) worth of jewellery when a gang of masked men burst into her apartment during Paris Fashion Week.
Most of those arrested were picked up in the Paris area, but raids were also carried out in the Seine-Maritime and Alpes-Maritimes regions. A jeweller in Paris is believed to have been searched.
Multiple firearms, including an automatic pistol, and €140,000 (£121,000) in cash were found during the raids.
The operation was co-ordinated by the Banditry Repression Brigade of the French police – a special unit in charge of armed robberies.
The robbers, wearing ski masks and dressed as police, broke into Kardashian’s apartment at around 3am on 3 October and held a gun to her head before tying her up and locking her in the bathroom.
They were let into the building near the historic Madeleine Church in the 8th arrondissement by the building’s concierge.
A police source said a jewellery box containing a ring worth €4m (£3.5m) had been taken along with other valuables worth between €5m and €6m (£4.4m – £5.2m).
According to police, the star was “badly shaken but physically unharmed”.
In the new series of Keeping Up With The Kardashians, she describes the moment she was attacked, saying through tears: “They’re going to shoot me in the back. There is no escape.”
The socialite returned to social media last week after taking a three-month break from the limelight following the incident.
The 36-year-old shared a picture of her alongside husband Kanye West and their two children, three-year-old daughter North and one-year-old son Saint.
The apartment where Kim was staying is said to have cost up to €15,000 (£13,000) a night.
She also stayed there before her wedding to Kanye West in 2014.
The rapper cut short a concert in the US following the raid.
In footage shot by members of the audience, he was heard saying, “I’m sorry, I have a family emergency. I have to stop the show” – before walking off stage.