(1) In recent years, an increase in the available functionality of non-ferrous alloys has been observed based on the modification and optimization of their chemical composition. This study investigated the effect of Sr addition on the structure and properties of hypereutectic Zn–Al–Cu alloys. The objective was to determine how a modification with Al–Sr master alloy affects the crystallization kinetics, microstructure, hardness, and abrasive wear resistance and whether the modification of the phase composition reduces the corrosion resistance. (2) The total influence of strontium was determined based on the microstructure, phase composition, and derivative curve changes of the tested Zn–Al–Cu alloys with added Sr. Optical microscopy, scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were used to analyze the influence of chemical and phase composition, and thermo-derivative analysis (TDA) was used to investigate the crystallization kinetics of zinc alloys with different chemical compositions. (3) Sr modification caused the formation of primary Al2Sr phases in the Zn alloy and also secondary Zn13Sr and Al4Sr phases (depending on the melting temperature of the alloy). (4) The primary and secondary intermetallic phases with strontium increased the hardness by approx. 20% and the abrasion resistance by approx. 7.5%.