The Mexican Military is the name given to the combined military forces of Mexico. So far, only ships and personnel of the Mexican Navy have been seen onscreen.
Fear the Walking Dead
In the episode Blood in the Streets, both Victor and Luis state that they have a contact who can help them get past the border and into Mexico. In the episode "Sicut Cervus" it is revealed that their contact is a member of the Mexican Navy, who is part of a small flotilla patrolling the coastal waters around Strand's intended destination in Rosarito, Baja California. They open fire on the Abigail after the gunfight between Luis and his contact.
From the conversation Strand and Luis had with their contact, it appears that the main aim of the flotilla that greeted the Abigail appears to be to keep infected ships from making landfall on Mexico's coast. It can be implied that the army is engaged in stopping the infected crossing over the border from the United States, since George Geary, mentions that Mexico had sealed its borders with the U.S. This may account for the lack of soldiers present after Strand and the others got onto land.
However, since there are known (small scale) outbreaks in Baja, it can be surmised that those members of the Mexican Military not involved in defending the border are engaged in similar operations to the U.S. Military in that they are trying to secure safe zones in the larger Mexican cities. It may also be possible that the country at large is overrun, explaining the lack of a large-scale military presence.
As season two progressed, it became evident that there is no military activity at all in the state of Baja California, as large groups of infected roam freely, only to confronted by members of various gangs. It is highly possible that the military in Baja suffered the same fate at the National guard in Los Angeles, in that they were completely overrun.
Evidence for the failure of the Mexican Military in Baja was implied early in the season, as after the shootout between Strand and his contacts, when asked why the other members of the flotilla didn't follow them or why they didn't try and sink The Abigail, he simply responds that those involved in the flotilla believe that whatever is on land would kill them.
In season 3, Strand finds the now beached Abigail, with the personnel on board who had commandeered her now dead and turned. What happened to the rest of the flotilla is unknown.
So far, only light costal craft of the navy have been seen on screen. However, they appear to be heavily armed as they were able to fire on the Abigail from a distance and do damage. The two officers who were the contacts for Luis and Strand carried side-arms, as they were able to engage in a brief firefight with Victor Strand and Luis.
It is implied that the military "acquired" The Abigail after Strand and the other survivors left the ship.