The masked assailants, who also threw stones and sticks at the bus at a red light in Istanbul's Sisli district Sunday, fled, Today's Zaman reported.
Passengers evacuated the bus as the blaze broke out, and the bus driver used the bus' fire extinguisher to put out the flames.
There were no reports of injuries.
The interior of the bus sustained substantial damage and the bus remains out of service.
Members of the Istanbul Police Department's counter-terrorism unit began an investigation and were searching for suspected members of the Kurdistan Workers' Party, known by its Kurdish-language initials PKK, which seeks an independent Kurdish state in southeastern Turkey.
The PKK is listed as a terrorist organization by Turkey, the United States and the European Union.