In this paper, the mechanical properties and minimum thermal conductivity of ZnZr, Zn2Zr, Zn2Zr3, and MgZn2 are calculated from first principles. The results show that the considered Zn-Zr intermetallic compounds are effective strengthening phases compared to MgZn2 based on the calculated elastic constants and polycrystalline bulk modulus B, shear modulus G, and Young’s modulus E. Meanwhile, the strong Zn-Zr ionic bondings in ZnZr, Zn2Zr, and Zn2Zr3 alloys lead to the characteristics of a higher modulus but lower ductility than the MgZn2 alloy. The minimum thermal conductivity of ZnZr, Zn2Zr, Zn2Zr3, and MgZn2 is 0.48, 0.67, 0.68, and 0.49 W m−1 K−1, respectively, indicating that the thermal conductivity of the Mg-Zn-Zr alloy could be improved as the precipitation of Zn atoms from the α-Mg matrix to form the considered Zn-Zr binary alloys. Based on the analysis of the directional dependence of the minimum thermal conductivity, the minimum thermal conductivity in the direction of [110] can be identified as a crucial short limit for the considered Zn-Zr intermetallic compounds in Mg-Zn-Zr alloys.