To answer this question accurately, it is important first to clarify a fundamental difference in legal philosophy: Mexico has never had "gun rights" in the sense that the United States does.
While the U.S. views the right to bear arms as an individual liberty protected from government infringement (via the Second Amendment), Mexico treats firearm ownership as a privilege granted by the state, which can be restricted or denied at the government's discretion.
Here is the breakdown of when and how Mexico’s restrictive gun laws were established.
1. The Constitutional Basis (Article 10)
The right to possess arms is mentioned in Article 10 of the Mexican Constitution. It states that citizens have the right to keep arms in their homes for security and legitimacy. However, this article also explicitly gives the Federal Government the power to regulate the types of arms, the calibers allowed, and the conditions under which they can be owned.
Because the Constitution itself grants the government total regulatory control, there was never a "transition" from wide-open rights to a ban; rather, the laws have consistently trended toward extreme restriction.