Tensions have been running high in recent months following a resurgence of extremist attacks in Bangladesh claimed by Al-Qaeda and the Islamic State group.
Last week the EU, which accounts for more than 60 per cent of Dhaka's USD 34 billion annual shipments, asked carriers transporting mail and cargo from the South Asian nation to provide an additional layer of screening to check for explosives.
"The screening can be performed either at the point of origin (Bangladesh) or at transit prior to the entry into the EU. The implementation will be the responsibility of the carriers/airlines," the EU delegation to Bangladesh said in a statement.
Its 4,500 textile factories are an economic mainstay, creating jobs for around four million workers.
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But it lacks explosive detection equipment, meaning goods for export may have to be scanned by a third country.
"The cost is not only the price but the time as well. It is a slap in the face of our image," Abdus Salam Murshedy, owner of Envoy Group, a leading garment exporter, told AFP.
Exporters fear any slowdown might prompt retailers such as H&M to divert orders to other nations, he added.
Last year Australia, Germany and the UK banned direct cargo shipments from Dhaka's international airport over security fears.
The country's civil aviation minister Rashed Khan Menon said the EU made the announcement "suddenly", with authorities taking steps to prevent any fallout.
"The installation of equipment (for explosive screening) may take another two months. Meanwhile, the delivery process may slow down a little bit," he told AFP.
Bangladesh's economy has been expanding at a fast clip, clocking growth rates of over seven percent two years in a row.