So it's a problem with your printer more generally, rather than Word itself. So presumably anything else you print, e.g. directly printing a webpage, will also print in greyscale.
Are the preferences set in the app you're using? I never use these kind of apps.
You can try and adjust the...
Presumably it's set to colour within the print setting within Word itself as well?
If you're using the 32-bit version of Office, you could try downloading the 64-bit version to see if it makes a difference.
Or email it to yourself and print direct from web. Or print as PDF (save as PDF from Word).