The Parliamentary Standing Committee on the Ministry of Civil Aviation and Tourism had summoned Jamal Uddin Ahmed to its meeting on Monday.
But he is away for performing Umrah in Saudi Arabia.
The flag carrier is under fire from the lawmakers over repeated seizures of smuggled gold at the airports.
Committee chief Muhammad Faruk Khan after the meeting told reporters that Ahmed’s absence had irked the panel members.
"There is no specific time frame to perform Umrah. He (Ahmed) didn't even notify anyone before going to Saudi Arabia."
Police in November arrested five people including one deputy general manager of Biman over their suspected involvement in gold smuggling.
Gold trafficking in Bangladesh has been on the rise, primarily because the country has emerged as a conduit for smuggling the precious metal into India.
The demand for gold in India is insatiable but higher duties imposed by the government to prevent outgo of foreign exchange have fuelled smuggling through Bangladesh.
Huge quantities have been seized at airports in both Bangladesh and India in recent months.