We obviously cannot know the future, but on what analysis is the minister's statement based?
The following was stated in the Bangladesh Climate Change Strategy and Action Plan of 2008:
If sea level rise is higher than currently
expected, and coastal polders are not strengthened
and/or new ones built, six to eight million people
could be displaced by 2050 and would have to be
resettled.
I could not find a more recent version of this document, but an academic working paper states the following:
The updated 2009 version addresses the issue of migration in more detail. It updates the figures of displacement due to sea level change, salinity, cyclones and storm surges at 20 million and seeks settlement of these ‘environmental refugees’, possibly abroad.
So the best way to evaluate the minister's statement might be to consult the 2009 document, but I was unable to find it.
Otherwise, the only reference I could find that might directly support the minister's statement was a story from Reuters:
Experts say a third of Bangladesh's coastline could be flooded if the sea rises one meter in the next 50 years, creating an additional 20 million Bangladeshis displaced from their homes and farms.
Note that says 50, not 40, and no specific source is cited.
A 2009 article in Scientific American gives a more conservatives estimate of 15 million people in Bangladesh displaced by the end of the century. Again, no source is given, but it is implied that this number may come from a trusted authority, IPCC, also mentioned in the original Guardian article.
The IPCC has quoted estimates that 5.5 million Bangladeshis would be exposed to land loss given a sea level rise of .45 meters, and 14.8 million if it is 1 meter. Thus if Bangladesh were to sea level rises well in excess of a meter within 40 years, the 20 million number might be in line with this particular projection. In fact, this seems a bit higher then most recent projections, but not wildly so.