Is an open container violation in Missouri just a fine? Or is it a points violation as well?

Missouri has no statewide vehicle open container law, thereby allowing passengers in motor vehicles (but not drivers) to consume alcohol openly, although 31 of Missouri's smaller municipalities do have local vehicle open container laws.

Typically of those, an open container offense is an infraction and not a crime, as such just a fine is imposed; there is no criminal record for pleading guilty. As for points, I could find nothing specific under state law.  What you should do now is to contact the DMV, or you can call a DUI attorney local to where the offense occurred, they could probably answer your question on the phone.