The Mexican Revolution was a messy conflict with various revolutionary factions holding different degrees of reformist beliefs. The Plan de San Luis Potosí, written by Díaz opponent Francisco I. Madero in 1910, didn’t call for major policy changes beyond Díaz’s removal and free elections (as well as a ban on presidential reelection), although it did promise to restore lands taken from peasants by Díaz’s land reform in 1894. It was essentially liberal in nature, and it was the vision that initially won out: after Díaz was ousted, Madero became president and continued many of his policies before his own removal in a counterrevolutionary coup led by General Victoriano Huerta, ending the first phase of the revolution.

The next phase was dominated by several figures, all allied under the “Constitutionalist” banner at times but who eventually became bitter rivals. Chief among them were Venustiano Carranza, Pancho Villa, and Emiliano Zapata. Of these, Zapata and his ideas were (in my opinion) the closest thing to socialism to achieve widespread influence during the revolutionary period. Zapata broke with Madero early on in the first phase of the revolution, and his Plan de Ayala called for massive land distribution towards peasants, which gained him a significant following in the poorer and more indigenous south of the country (where his army was already engaging in significant agrarian reform) and inspired the modern day Zapatista movement.

Zapata himself was not a socialist, but his legacy has been a major influence on the Mexican left, and his control over the south gave him significant influence on the revolutionary constitution (written after Huerta was defeated by the Constitutionalists), which enshrined state control over agricultural land and the system of ejidos, or communal plots of farmland. However, another Constitutionalist leader, Gen. Venustiano Carranza, defeated Zapata and his then-ally Pancho Villa in the wake of the toppling of Huerta. Carranza had only begrudgingly agreed to engage in redistribution of agricultural land and accept the reforms Zapata and Villa had already made, which they saw as a betrayal and led to them turning on the new government, but Carranza’s army was victorious. Carranza and his followers, namely Alvaro Obregón, were the ones who consolidated power after the revolution, founding what would become the dominant (and dictatorial) Institutional Revolutionary Party. While the party did support some efforts at land reform and produced a very progressive constitution for its time, it was less radical than the zapatistas and villistas were and did not pursue large-scale redistribution of land or other wealth after the 1910s.

Tl;dr: it wasn’t, but some revolutionary elements were more socialist than others, and land reform (akin to those enacted by later revolutionary leftist governments in Guatemala and Bolivia) was a key element of economic policy during the revolution.

Edit: there were also more explicitly socialist revolutionaries in some areas, such as the anarchist Flores Magón brothers in Baja California, but they never gained the level of popular support or influence that Zapata, Villa, or Carranza and the eventual victors had.