Benapole is the busiest land port, through which much of the bilateral trade between the two neighbours takes place.
Port authorities said one of the sheds at the warehouse caught fire around 6am on Sunday.
Witnesses said they spotted smoke billowing out of the shed and then the fire spread to the police station of the port.
The port's fire service unit immediately started fighting the flames and were later joined by six others fire-fighting units from Jessore.
The fire also gutted goods kept beside the shed under the open sky and also three trucks parked near it.
"There have been similar cases of fire erupting mysteriously in the past and every time the port authorities blamed it on electrical malfunction," said Benapole Clearing and Forwarding Agents Association President Mafizur Rahman Sazan.
The port authority has formed a three-member body to probe the incident.
According to official statistics, between 70 to 80 percent of India-Bangladesh bilateral trade through land happens by the Benapole port.
As many as 1.2 million people travel between the two countries through the port every year.