Police swooped in the Paris region and the south of France following forensic work at the luxury Paris residence where Kardashian was tied up and robbed of jewellery worth around nine million euros ($9.5 million) in October, one of the sources told AFP.
"One of the DNA samples matched an individual known to police for robbery and criminal offences, who is considered a major thug," the source said.
Using the evidence found at the scene, investigators were able to put in place a surveillance operation and build up a picture of the criminal network behind the robbery, he said, adding that it stretched to Belgium.
Money and documents were also seized in Monday's raids.
A gang of armed and masked men wearing police uniforms had burst into the residence in the chic Madeleine area of the capital where 36-year-old Kardashian and her entourage were staying during Paris Fashion Week.
The gang tied up Kardashian, locked her in the bathroom and fled with jewellery including a ring worth around four million euros and a case of jewellery with a value of five million euros.
The Kardashian family's French bodyguard Pascal Duvier was not at the scene at the time because he was providing security for Kim's sister Kourtney at a Paris nightclub.
- 'Shoot me in the back' -
Kardashian, who is married to rap mogul Kanye West, finally broke her silence about the incident this weekend, saying she feared she was going to be killed by the robbers.
"They're going to shoot me in the back," she sobbed to her sisters while recounting the ordeal in a promotional clip for the new season of her TV show "Keeping Up with the Kardashians".
"There's no way out. It makes me so upset to think about it," she added.
It is believed the men escaped on bicycles but one of the gang dropped a diamond pendant worth around 30,000 euros in the street outside.
It was found by a passer-by and handed in to police several hours after the robbery.
Kardashian lodged a formal complaint in France after she was filmed fiddling with her mobile phone at the residence immediately after the robbery.
Her lawyers said in October the video was made "without her consent or the police's and while the police were investigating the crime scene".
It emerged afterwards that Kardashian had raised the alarm after untying herself and calling her bodyguard.
Kardashian has harnessed the power of social media to rise to fame, with nearly 50 million followers on Twitter and 90 million on Instagram.
A month after the Kardashian robbery, two Qatari women were held up on a motorway outside Paris and robbed of valuables worth more than five million euros.
The women, in their sixties, had just left Le Bourget airport northeast of the capital when their chauffeur-driven Bentley was held up by two masked men who sprayed them with tear gas.