The plaintiff named only as Mohsin filed the case with Chittagong Additional Chief Judicial Magistrate ASM Shahidullah Kaiser's court on Thursday, four days after the incident.
This is seen as a counter-case as a pro-BNP lawyer sued local leaders and activists of the Awami League for attacking Fakhrul's motorcade.
Mohsin alleged that the motorcade of the BNP leader hit two auto-rickshaw drivers in front of Rangunia Upazila Health Complex on Sunday morning, said Nikhil Kumar Nath, the lawyer for Mohsin.
Nikhil told bdnews24.com that the BNP leaders and activists in the motorcade beat up locals who rushed to the rescue of the injured drivers. They also vandalised the auto-rickshaws, Mohsin said in the case under Speedy Trial Tribunal Act.
The magistrate ordered the Police Bureau of Investigation to investigate the case and submit a report within July 19.
The accused include Rangunia BNP Convenor Shawkat Ali Noor, Joint Convenor Nizamul Haque Swapan and former organising secretary Yusuf Mia.
On Wednesday, another case was initiated against 26 local leaders and activists of the Awami League on charges of attacking Mirza Fakhrul's motorcade. PBI is investigating that case too.
The BNP alleged that local Awami League MP Hasan Mahmud's supporters carried out the attack.
Mahmud said locals attacked the BNP leader's motorcade after one of its vehicles hit two.