This is a strange one. I have several document libraries that I have successfully uploaded all sorts of documents until today.
I was attempting to upload a Word document however SharePoint rudely rejected the action stating "The file name is invalid or the file is empty...", screen shot attached.
I can upload .txt files, .js files Excel files, even .png with no problems. It took awhile but I figured out the error was due to the Word document being empty. That's right, SharePoint will not upload an empty Word document via browse. It will upload an empty Excel file though. *scratch's head*
Now if you absolutely have to upload an empty Word document, you can use Explorer mode as a work around.