The accident took place early on Sunday after the driver of one of the buses fell asleep at the wheel, the Dhaka Tribune newspaper reported, citing the local police and survivors.
"We and some other passengers had warned him multiple times. The accident happened because the driver fell asleep and lost control," one of the survivors was quoted as saying.
The local fire service has launched rescue operations, the newspaper said, adding that the bus driver was among the victims.
Six of those injured were in critical condition, while some 30 of them were discharged from hospital after receiving first aid, the newspaper added.