Police said the four-wheel drive vehicle struck pillars and barriers protecting the mosque of Créteil, south-east of the capital, before speeding off and crashing into a traffic island. No-one was injured.
The driver, who sources say is a 43-year-old Armenian who owned the vehicle, fled the scene.
But he was arrested "without incident" at his home shortly afterwards, police said.
French Interior Minister Gérard Collomb said in a statement that the man's "exact motives" will be determined by an investigation.
A search was conducted Thursday night at the driver's home, according to sources close to the investigation who also said the suspect had made confused remarks in relation to jihadist attacks that have struck France, killing 239 people since 2015.
According to judicial authorities, he was not under the influence of alcohol and will undergo psychiatric tests.
Paris police prefect Michel Delpuech said he was "doing everything possible... to clarify the motives of the driver and determine if he is criminally responsible".
The head of the National Observatory Against Islamophobia, Abdallah Zekri called for "more vigilance on the part of mosque officials" and asked authorities to "strengthen protection of places of worship".
"What has just happened in Créteil seems to justify the fears I expressed after the attack close to Finsbury Park mosque in London," Zekri told the AFP news agency, referring to the 19 June mowing down of worshippers leaving the north London place of worship.