The minimum width is generally respected by Facebook, and should be 292px or greater. However, we've seen it work down to about 270px, I think.
The minimum height is variable. The header is a fixed amount. Once you add the stream, it takes up a lot of space, but also makes the module 'grow' to as big of a container that you put it in. So, if you're using the avatars and/or stream, the minimum height will grow. I don't know the exact dimensions for those fields though, you'd have to test enabling/disabling some of the features to determine what works best for the area you have available.
I hope that helps,
Alex