Zunaid Ahmed Palak, state minister for posts, telecommunications and Information Technology of the recently ousted Awami League government, was detained at Hazrat Shahjalal International Airport on Tuesday.
He was attempting to flee to New Delhi, India, according to media reports.
An official at the airport said he had been detained by staff and workers.
Sheikh Hasina resigned as prime minister on Monday afternoon in the face of nationwide protests, before fleeing the country.
Chief of Army Staff General Waker-Uz-Zaman later in the day addressed the nation announcing that an interim government would soon be formed.
Since then, reports have emerged of several ministers' and senior Awami League leaders' escape.