The ideal way to do it is probably to embed it as an OLE object.
In theory, this is quite easy. But when I tried doing it with a PDF, I found things didn't work as expected. See further How to create an oleObject.bin
If you are lucky, Visio embedding will be easier than PDF embedding. Try it and let us know how you go. To get a feel for what you are aiming for, drag your visio object into a Word document, then save the .docx (or easier .xml flat opc), then open it and have a look at the result. Unless you save as .xml, you'll need to unzip or use Package Explorer or docx4all view source to see the xml
A possible alternative would be to export the Viso object as say a png, and add that image to your document.