Traffic was disrupted in some parts of the country as protesters tried to set up roadblocks using burning tyres.
Several passenger vehicles were also set on fire in various parts of Bangladesh in the run up to the protest.
A 60-year-old driver of a passenger bus was killed by smoke inhalation after people set fire to the vehicle in the city of Faridpur early on Tuesday.
Elsewhere, about 200 protesters briefly blocked traffic on the 6.2km (4 mile)-long Padma bridge across the Ganges, that connects the capital Dhaka with the south-western region.
Bangladeshi local media said dozens of crude bombs exploded in the past few days in Dhaka and elsewhere.
“Any attempt to worsen the law-and-order situation or create instability through any conspiracy within the country from across the border (India) will not be allowed to succeed,” Bangladesh Home Minister Salahuddin Ahmed said.
“Our supporters were not responsible for the violent incidents. They were carried out by unknown miscreants. We believe in peaceful protests,” a senior leader of the BCL, who is now in exile in a foreign country, said.
Hasina fled to neighbouring India two years ago following a massive uprising, bringing an end to her 15-year reign.
Opposition parties accused Hasina of jailing political rivals, supressing dissent and overseeing widespread human rights abuses. She always denied the charges.
