This study investigates the effects of extrusion temperature on the microstructural characteristics and mechanical properties of an extruded Mg–9Al–0.8Zn–0.9Ca–0.6Y–0.5MM (AZXWMM91100) alloy and the resulting unusual relationship between the extrusion temperature and the tensile strength of the extruded material. All the extruded materials, i.e., alloy samples extruded at 325 °C, 350 °C, and 400 °C, have a fully recrystallized grain structure and contain abundant undissolved Al8Mn4Y, Al2Ca, and Al2Y particles. A small number of spherical nanosized Mg17Al12 precipitates are formed during extrusion, and their number density decreases with increasing extrusion temperature. The undissolved-particle bands, which are distributed parallel to the extrusion direction, act as obstacles to the growth of recrystallized grains during and after extrusion, which prevents excessive coarsening of grains at high extrusion temperatures. As a result, despite a large increase in the extrusion temperature from 325 °C to 400 °C, the average grain size of the extruded material increases only slightly, from 17.6 µm to 23.0 µm. Concurrently, the tensile strength of the extruded material increases from 183 MPa to 224 MPa; this directly proportional relationship between temperature and strength contrasts with the general inverse relationship between extrusion temperature and tensile strength. An increase in the extrusion temperature leads to an increase in the texture intensity of the extruded material; this increase is attributed to the following phenomena: (i) transition of the dominant dynamic recrystallization (DRX) mechanism from twinning-induced DRX and continuous DRX to discontinuous DRX, (ii) weakening of DRX through particle-stimulated nucleation, and (iii) promotion of the activation of prismatic slip. Therefore, the unusual extrusion temperature–tensile strength relationship for the AZXWMM91100 alloy is a combined result of the grain coarsening suppressed by the undissolved particles and strengthening of the texture hardening effect with the variation in the DRX behavior during extrusion.