First-principle calculations are carried out to explore magnesium composition-dependent structural and optoelectronic features of wurtzite Mg$_x$Zn$_{1−x}$Se ternary alloys. Analyses show a nearly linear enhancement in lattice constants (a0, c0) but a reasonably nonlinear reduction in bulkmodulus (B0)with increasingMg composition. Successive incorporation of Mg atom(s) in place of Zn in the w-ZnSe crystal results in three direct-band gap ($\Gamma–\Gamma$) semiconductor ternary alloys. The fundamental band gap shows fairly nonlinear enhancement with increasing Mgcomposition. Each of the considered wurtzite specimens is optically anisotropic. The computed components of the refractive index give uniaxial birefringence. Peaks in the dielectric function spectrum of all the specimens in the ultraviolet (UV) region are contributed exclusively or collectively by Se-4p to Mg-4s, 3p and Zn-5s, 4p electronic excitations. With the enhancement in the fundamental band gap, static optical constants ε1(0), n(0) and R(0) of the specimens reduce, while critical point energy in their ε2(ω), k(ω), σ(ω), α(ω) spectra enhances.