Yes, there is a way, just not from Obsidian. Pandoc does it, rather well in my experience.
pandoc test.md -f markdown -t docx --bibliography=test.bib --csl=chicago-fullnote-bibliography.csl -s -o test.docx
(You can of course change the csl to whatever you want to.)
It’s really worth installing pandoc if you don’t have it yet; I also hate working with docx files, but this way you can get them from markdown, latex, whatever. (You do need a .bib file though; I don’t know about the alternatives there.)
@ryanjamurphy, there could be some plugin or something in Obsidian that would parse a given .bib file and probably via pandoc produce a .docx output. I’m no programmer so absolutely no clue what this would take, but doesn’t seem impossible if it’s doable through the command line.