At I/O this year, Google promised support for the Korean language would be coming by the end of the year to Assistant. Then at the October Pixel event a couple of weeks ago, Google also stated that Actions on Google (third-party Assistant integrations from different services) now support Korean. Between then and now, it appears that support for the Korean language has gone live on Assistant.
Google's help pages now say that you can talk to Assistant in Korean on your phone, your Wear watch (which makes sense since it's connected to your phone), and that developers can add it in their Actions on Google apps. However, since Google Home hasn't launched in South Korea yet, the Korean language isn't yet supported on Google Home (or speakers with Assistant or TV). The most bewildering thing though is that the support docs say it's not supported in Allo. I mean if it's working on the phone, what's the difference? Eh, Google?
The Allo Assistant support page was just updated to add Korean as a supported language, so you can now expect smart answers and contextual information inside Allo when you're typing and speaking in Korean.
Anywho, if you've set your phone to the ko-KR language, Assistant should have either shown itself to you or will soon. If you haven't gotten it yet, try tapping and holding the home button on your phone to see if it switches from Now on Tap / Screen Search to Assistant.