Short answer. Possibly, if the insult rises to the level the Labor Code describes. It lets an employee end the relationship without notice for a serious insult by the employer or a representative on the employee's honor and person. Whether a particular insult qualifies as "serious" is the real question, not merely that it happened in public.
What the law says
Serious insult by the employer or his representative on the honor and person of the employee
Labor Code, Article 285 — Resignation By The Employee. Read the full provision →
This is one of the listed just causes for immediate resignation
Article 285 generally requires an employee to give at least one (1) month written notice before resigning. It then lists specific just causes that let an employee put an end to the relationship without serving any notice. The first of these is serious insult by the employer or his representative on the honor and person of the employee — a direct match for being insulted by your boss, provided the insult meets what the article describes.
The word "serious" is doing the real work
The article does not say any insult qualifies — it specifically requires a serious insult, and one directed at your honor and person. That framing points toward something more than an ordinary sharp comment or criticism; it is aimed at insults that attack your dignity or standing as a person. The article gives no further definition of what crosses that line, leaving the specific words used and the manner of the insult to determine whether it fits.
Public humiliation is relevant, but the article's test is about the insult itself
Being insulted in front of coworkers can make an insult more humiliating, but Article 285's own language is framed around the insult being serious and directed at your honor and person — it does not separately list "done in public" as its own qualifying factor. The setting can be part of the overall picture, but it is the seriousness and target of the insult itself, on the article's terms, that determines whether this ground is available.
What to keep track of
If you are considering resigning without notice on this ground, write down exactly what was said, when, and who witnessed it, as close to the incident as possible. Since the article turns on whether an insult was serious and aimed at your honor and person, the precise words and circumstances are what will matter most in showing your situation fits within this specific just cause. The consequence for guessing wrong sits in the article's own first sentence: an employer who receives no notice may hold the employee liable for damages. If a later dispute concludes the insult did not rise to the level of "serious," you resigned without the one-month notice the article otherwise requires, and that exposure to a damages claim is what you would be relying on the just-cause exception to avoid.