I'm just a few points above what's needed to run Civ 5, and yet it runs absolutely beautiful, so long as I turn the shadows off. I think a small upgrade will help, but you might be fine. It is, after all, too early to tell.
My PC is just above the minimum specs for Civ 5. Will it be able to run CivBE, or do I need to upgrade?
If it runs Civ V in DX11 mode, then it will probably run since its the same engine. (Any graphical glitches you have on DX11 are likely for BE for the same reason.)
If it only runs Civ V in DX9 mode, then it doesn't look like it will run BE since it looks like they aren't including a DX9 version executable.
Note that late game slowness issues in Civ V may be much more of an issue with BE because there are less penalties to self expanding wide and in fact one of the victory conditions (Purity) requires space to set up the colonists coming thru the wormhole.
If it only runs Civ V in DX9 mode, then it doesn't look like it will run BE since it looks like they aren't including a DX9 version executable.
My graphics card is a GT640 DDR3 with 1 Gig of memory. Will that be sufficient for CivBE?
Why no DX9?
If you aren't running Win 7 64-bit on a 64bit machine with a reasonably (say 2-3yr old at most) new graphics card (not onboard graphics), then expect to have issues with most games in the next few years.
Worse than that, they aren't even doing a DX12 version for the 64 bit Windows 7 but appear to be trying to force people into downgrading from Windows 7 to Windows 8 if they want DX12. (I actually expect the game developers to revolt over this when it gets closer to release DX12 release, there will probably be so many people still with Windows 7 machines that the game developers won't want to be cut out of the market for.)