The comments in the documentation indicate this attribute is converted into part of the assembly's name and not part of the assembly's metadata. Weird. It does suggest using the GetName() method to get the AssemblyName, which includes a Version property:
Code:
Public Function GetVersion() As Version
    Dim assem = Assembly.GetEntryAssembly()

    Dim name = assem.GetName()
    Return name.Version
End Function
That seems to work.