A common misconception is that firearms are illegal in Mexico and that no person may possess them.[3] This belief originates due the general perception that only members of law enforcement, the armed forces, or those in armed security protection are authorized to have them. While it is true that Mexico possesses strict gun laws,[4] where most types and calibers are reserved to military and law enforcement, the acquisition and ownership of certain firearms and ammunition remains a constitutional right to all Mexican citizens and foreign legal residents;[5] given the requirements and conditions to exercise such right are fulfilled in accordance to the law.[6]

https://en.wikipedia.org/wiki/Gun_laws_in_Mexico

So they're restricted, more strongly than in the US, but not banned.