Mohammed Nasim told Parliament on Thursday that around 33,000 people had been affected by swine flu in India.
Of them, nearly 2,000 have died, he said.
Nasim said neighbouring West Bengal state had identified over 200 swine flu cases, of whom 24 had died.
"As Bangladesh is surrounded by India and over 1,000 people cross the border every day, Bangladesh is at risk of the disease spreading," he said in reply to a query.
He also spoke about the government's steps to prevent swine flu.
After the 2009 outbreak, swine flu became a “seasonal influenza” (H1N1) in Bangladesh like the other two viruses --influenza B and H3.
A combined vaccine against these three viruses is available, a single shot of which can help high-risk groups like pregnant women, serious diabetics, and cancer patients.
Bangladesh last recorded a swine flu case in April 2013.