In the case of technologically important Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary alloys, structural and optoelectronic properties have been calculated with density functional theory (DFT)-based full-potential linearised augmented plane-wave (FP-LAPW) approach. The Perdew–Burke–Ernzerhof generalised gradient approximation (PBE-GGA) for structural properties and both the modified-Becke–Johnson (mBJ) and Engel and Vosko GGA (EV-GGA) for optoelectronic properties are employed to calculate the respective exchange-correlation potentials. Each specimen within the Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary system is a direct band-gap ($\Gamma$-$\Gamma$) semiconductor. The lattice constant decreases, while bulk modulus and band gap increase nonlinearly with increasing anionic (S) concentration $y$ at each cationic (Mg) concentration $x$. On the other hand, nonlinear increment in lattice constant and band gap, but decrement in bulk modulus is found with increase in cationic concentration $x$ at each anionic concentration $y$. Calculated contour maps for lattice constants and energy band gaps would be useful in fabricating new quaternary alloys with preferred optoelectronic features. Optical properties of the specimens within the Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary system show several interesting features. Chalcogen-p→Zn-5s, 4p and chalcogen-p→Mg-4s, 4p optical excitations contribute intense peaks in each $\varepsilon_2(\varepsilon)$ spectrum. The composition dependence of each calculated zero-frequency limit shows opposite trend, while each calculated critical point shows similar trend of composition dependence of band gap. Moreover, calculations suggest the possibility of growth of several cubic Mg$_x$Zn$_{1-x}$S$_y$Se$_{1-y}$ quaternary specimens on GaAs and InP substrates.