He said five million doses of vaccine per month would be purchased through Bangladesh's drug maker, Beximco Pharmaceuticals.
"We'll be able to vaccinate 15 million people as two shots of vaccine are required for each person 28 days apart," Maleque said.
Bangladesh was in talks with development partners, including the World Bank and Asian Development Bank, to secure funds for the vaccine, government officials said.
Meanwhile, Sinovac Biotech's late-stage trial of a potential coronavirus vaccine in Bangladesh has become uncertain after Dhaka refused to meet the Chinese company's demand for co-funding.
Experts fear Bangladesh might face another surge in infections during the winter, having so far confirmed 416,006 cases, including 6,021 deaths.
The Serum Institute, the world's largest manufacturer of vaccines by volume, has partnered with AstraZeneca, the Gates Foundation and the Gavi vaccine alliance to produce more than a billion doses of a covid-19 vaccine for global supply.
It is holding trials for three potential coronavirus vaccines, including one licensed to AstraZeneca by Oxford University.
AstraZeneca has signed several supply and manufacturing deals with companies and governments around the world, while data in October showed the vaccine produces a immune response in both old and young adults.