The suspects were picked up in the Paris region and are now in custody, a police source told AFP.
The attack on the prince's convoy took place in August in northern Paris as the motorcade was making its way from a plush hotel on the Champs Elysees to an airport in Le Bourget.
A gang of "between five and eight" thieves in two BMWs hijacked the first of around 10 vehicles in the convoy, driving off with the three occupants before letting them go, police said.
Police found two 500-euro notes, documents in Arabic, and medication near the burnt-out wrecks of the two cars. The thieves also made off with "sensitive" diplomatic documents.
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At the time, police described the attack as "unusual" and stressed that assailants were "obviously well-informed."
No one was hurt in the attack.
Airport sources said the prince was Abdul Aziz Bin Fahd, the multi-millionaire youngest son of King Fahd, who died in 2005.