He and others on the car were unharmed in the alleged attack near Kanjorparha bridge at Teknaf's Hoaikyong around 9:30pm on Friday.
A shot was fired at the moving car, Bodi told bdnews24.com.
“I was fortunate to survive,” he said.
Police, however, are not sure whether a gunshot was fired or a brickbat hurled.
Additional Superintendent of Police Md Iqbal Hossain said the rear window of the car was shattered.
Besides Bodi, his chauffer and Farid Alam, a former councillor of Teknaf municipality, were in the car.
“We are investigating the incident,” the additional SP said.
Bodi said he was preparing to start a case over the alleged attack.
Without naming any person, Bodi also alleged a BNP leader was trying to destabilise the atmosphere ahead of the parliamentary elections.
His wife Shahina Akhter is contesting as the Awami League candidate for the Cox’s Bazar-4 constituency in his stead.
The ruling party dropped Bodi from the race due to his alleged involvement in the smuggling of yaba from Myanmar.