Constrained Friction Processing (CFP) is a novel friction-based technique designed for the processing of rods from lightweight materials such as Al and Mg alloys. The CFP appears as a suitable technique to overcome the processing limitations of Mg alloys associated with the poor workability and low ductility intrinsic to the hexagonal closed-packed (hcp) structure. CFP is performed by plunging the rotating shoulder into the workpiece, which causes the extrusion of the material into the tool cavity. Simultaneously, this material is constrained by the rotating probe. The material flow developed during the process is a result of the friction between shoulder and material, and the subsequent large strains and temperature rise conditions lead to the dynamic recrystallization of the material, resulting in a fine- (or ultra-fine) microstructure. The aim of this work is to present the correlation between the material flow conditions to the development of the microstructure in terms of grain refinement and texture of rods processed from AM50 alloy, and ultimately, its mechanical properties. The results show that the grain size slightly varies according to the position of analysis along the rod as a function of the heat explosion of each portion of material, having the most refined grains at the bottom of the rod and the largest grains near to the interface between shoulder and material being processed. Moreover, a clear influence of the material flow is observed in the crystallography orientation of the material, indicating the effect that the (0002) basal planes of the Mg’s hcp structure are aligned to the shearing direction, resulting in a local texture gradient along the rod’s radius. Microtensile tests using specimens taken at different positions along the rod indicate a drastic difference in the mechanical properties depending on the position of observation, hinting that the texture has a major effect on properties such as yield strength and ductility.