The attacks were carried out within 35 minutes, using small cooking gas canisters to burn the cars, all bearing diplomatic license plates, the police and fire service said.
Two of the cars were used by staff at the Turkish embassy, the others from the embassies of Italy and the Philippines.
No one was hurt and there was no immediate claim of responsibility. In one of the incidents, the fire spread and damaged a fifth car.
Anarchist groups in the capital frequently carry out arson attacks, typically targeting banks, international companies, politicians' offices and diplomatic cars, but their activity had halted in recent months.