This works for me (Excel 2013):
Public Sub StartExeWithArgument()
Dim strProgramName As String
Dim strArgument As String
strProgramName = "C:\Program Files\Test\foobar.exe"
strArgument = "/G"
Call Shell("""" & strProgramName & """ """ & strArgument & """", vbNormalFocus)
End Sub
With inspiration from here https://stackoverflow.com/a/3448682.