A source says authorities are trying to establish whether the driver passed on information to the gang who raided her apartment.
French media reported that DNA traces picked up off the tape used to tie up Kardashian led police to the suspects, who could be questioned for up to four days.
Jean Veil, a French lawyer for Kardashian, told France 2 television: "She (Kardashian) is very happy, very satisfied and to a certain extent reassured by the efficiency of the French police."
One of the people arrested over the theft of around €9m (£7.8m) in jewels from Kim Kardashian West is a chauffeur who drove her around Paris before the robbery.
The reality TV star had a gun held to her head before being tied up and locked in the bathroom while the robbers, who wore ski masks and clothes with police markings, made off with the jewellery.
A police source said a jewellery box containing a ring worth €4m (£3.5m) had been taken, along with other valuables worth between €5m-€6m (£4.4m-£5.2m).
A total of 17 people were arrested in raids across France on Monday, many of them known underworld figures aged around 50, police and judicial sources said.
The oldest suspect held is a 72-year-old man held in the Provencal city of Grasse, while the youngest is in his early 20s.
Three women were among those detained, including one aged 65 who was arrested in the southern region of Gard, according to a source close to the investigation.
Multiple firearms, including an automatic pistol, and €140,000 (£121,000) in cash were found during the raids.
A police source told Reuters that authorities were trying to establish whether the chauffeur, who ferried Kardashian around the French capital during Paris Fashion Week, passed on information to the gang.
Jean Veil, a French lawyer for Kardashian, told France 2 television: "She (Kardashian) is very happy, very satisfied and to a certain extent reassured by the efficiency of the French police."
Kardashian was unharmed in the robbery, but badly shaken up.
She has mostly kept a low profile since the ordeal, but broke her silence in a promotional clip for the upcoming season of Keeping Up With The Kardashians, which was released on Friday.
"They're going to shoot me in the back. There's no way out," a tearful Kardashian tells her family, recalling what happened.
"It makes me so upset to think about it."
She also returned to social media last week after taking a three-month break 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.
