Judge Judy -- Judge Joe Brown Needs to 'Stay Sober'

Judge Judy seems to think Judge Joe Brown's arrest last month had nothing to do with politics ... but more about hitting the bottle.

TMZ caught up with Judy outside of Craig's in West Hollywood last night, and when we asked if she had any words of wisdom for Joe ... she simply said, "Stay sober."

Now ... our photog was asking because of Joe's notorious courtroom meltdown ... but it's possible Judy was thinking more about the video that surfaced last August of Joe drunkenly interacting with a group of fans.

Either way ... Judge Judy has spoken.