"We're on alert as a precautionary measure against the H1N1 influenza," Benazir Ahmed, director of disease control under the ministry of health and family welfare, told Xinhua.
A ministry official said they were asked to remain on alert after media reports said at least 494 cases of swine flu and 95 deaths were reported in India since January.
"We're closely monitoring the influenza situation in India so that we can go for more preventive measures like establishing checkpoints on borders on a short notice," Ahmed said.
The government has urged people not to panic but be cautious about the outbreak.
A/H1N1, which first appeared in Mexico in 2009, has rapidly spread around the world.
With the death of two women in 2010, the toll in Bangladesh has risen to eight since the first A/H1N1 case in June 2009.
The respiratory virus, which infects pigs and humans only sporadically, spreads mainly through coughs and sneezes.
Since 2009, Bangladesh has reported 783 A/H1N1 flu cases, including 150 in 2012, said Alamgir Hossain from the Institute of Epidemiology, Disease Control and Research under the health ministry.
"There is nothing to be scared of because we're now better prepared to treat patients infected with the virus," Hossain said.
He said officials from all 26 surveillance sites across Bangladesh will sit together to discuss a mechanism to better combat the disease.