Fakhrul's motorcade had come under attack at Rangunia on Sunday morning while he was on his way to Rangamati to meet people affected by the deadly landslides.
Later, the seven-strong BNP delegation returned to Chittagong from there.
Senior BNP leader Amir Khosru Mahmud Chowdhury, who was accompanying Fakhrul, said both he and Fakhrul were injured in the attack.
"I've talked to the IGP about the incident and asked him to find the culprits following a neutral investigation," he said.
The minister was speaking to journalists after inspecting the activities of a BRTA mobile court in front of Radisson Blu hotel on the Airport Road in Dhaka.
The BNP has also put the blame on Awami League leader Hasan Mahmud and his supporters for the attack and announced nationwide protests on Monday.
Mahmud, a local MP and the ruling party's publication secretary, however, alleged that the car carrying the BNP secretary general hit two persons in Rangunia's Ichhakhali.
"The agitated locals attacked them," he told bdnews24.com.