The three private airliners are US-Bangla Airlines, Novoair and Regent Airways.
India on Wednesday announced the suspension of all existing visas, except diplomatic, official, UN/international organisations, employment and project ones, till April 15.
Tahera Khandakar, deputy general manager (public relations) of Biman, said they have decided not to operate any flight during the period.
She also said passengers who haves already bought tickets will get refund or can travel once the ban is withdrawn.
Novoair Senior Manager Mahfuzul Alam also echoed Tahera.
Meanwhile, General Manager (public relations) of US-Bangla Airlines Kamrul Islam told UNB that they will maintain complete flight suspension from March 17.
They will operate flights from Chennai to Dhaka till March 14 and from Kolkata to Dhaka till March 16, he said.
Regent Airways Director Sohel Majid said their flights will bring Bangladeshis from Kolkata till March 15.
However, the aircraft will carry no passenger while going there, he added.