The incident took place around 9:30 am Friday when the ferry, named Shah Jajal, was on its way to the Shimulia terminal from Banglabazar in Madaripur.
BIWTC authorities have temporarily suspended Abdur Rahman, the ferry in-charge and inland master officer, due to his failure to properly operate the vessel.
"The ferry hit pillar No. 17 of the Padma bridge while crossing the river along the Banglabazar-Shimulia route, leaving several people injured but the pillar was largely undamaged," Jahangir Alam Khan, a spokesman for the shipping ministry, told bdnews24.com.
The river had been turbulent since Friday morning and the ferryman lost control of the vessel due to a combination of inclement weather and high tides while entering the river, according to one of the passengers.
"The collision left a large dent on the front end of the ferry," BIWTC's Assistant General Manager Shafiqul Islam said.
"The ferry was carrying 33 vehicles and more than 2,000 passengers. The vehicles collided against each other on impact. Many passengers fell on the deck of the ferry."
The ferryman did eventually regain control of the vessel and managed to guide it to the Shimulia port without any incident afterwards.
Rahman, the ferry operator, later said the vessel's electronic system had failed during the crossing. He managed to fix the problem immediately but not before the ferry hit the pillar.
"The ferry could have sunk if the collision occurred below the river's water level," he said.
The injured are receiving treatment at various hospitals near the port.