A possible approach is like this,
1 Programmatically printing git revision and checking for uncommitted changes
Following this post to learn how to query revision information from the working copy.
2 Modify your VB.NET project file so that before compiling it uses the query result above to update one of your file to include this information to your executable.
The second step needs some scripting skills. If you are familiar with MSBuild scripting, it should not be too hard.
Personally, I may write my own console application in .NET to perform the above commands, and then include it in PreBuild event.