Eu-based Zintl-phase materials $\mathrm{Eu}{A}_{2}P{n}_{2}$ $(A=\mathrm{Mg},\mathrm{In},\mathrm{Cd},\mathrm{Zn};Pn=\mathrm{Bi},\mathrm{Sb},\mathrm{As},\mathrm{P})$ have generated significant recent interest owing to the complex interplay of magnetism and band topology. Here, we investigated the crystallographic, magnetic, and electronic properties of layered Zintl-phase single crystals of ${\mathrm{EuMg}}_{2}{\mathrm{Sb}}_{2}$ with the trigonal ${\mathrm{CaAl}}_{2}{\mathrm{Si}}_{2}$ crystal structure (space group $P\overline{3}m1$). Electrical resistivity measurements complemented with angle-resolved photoemission spectroscopy (ARPES) studies and density functional theory (DFT) calculations find an activated behavior with intrinsic conductivity at high temperatures indicating a semiconducting electronic ground state with a narrow energy gap of 370 meV. Magnetic susceptibility and zero-field heat capacity measurements indicate that the compound undergoes antiferromagnetic (AFM) ordering at the N\'eel temperature ${T}_{\mathrm{N}}=8.0(2)$ K. Zero-field neutron-diffraction measurements reveal that the AFM ordering is A type, where the Eu spins (${\mathrm{Eu}}^{2+}, S=\frac{7}{2}$) arranged in $ab$-plane layers are aligned ferromagnetically in the $ab$ plane and the Eu spins in adjacent layers are aligned antiferromagnetically. Eu-moment reorientation within the $ab$ planes in the trigonal AFM domains associated with a very weak in-plane magnetic anisotropy is also evident below ${T}_{\mathrm{N}}$ at low fields of $<0.05$ T. Although isostructural semimetallic ${\mathrm{EuMg}}_{2}{\mathrm{Bi}}_{2}$ is reported to host Dirac surface states, the observation of narrow-gap semiconducting behavior in ${\mathrm{EuMg}}_{2}{\mathrm{Sb}}_{2}$ implies a strong role of spin-orbit coupling (SOC) in tuning the electronic states of these materials. Our DFT studies also suggest that introducing the more electronegative and smaller Sb in place of Bi, besides reducing the SOC, shifts the low-lying conduction bands along the $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}\mathrm{A}$ direction to higher energy, resulting in an indirect bulk band gap between the $\mathrm{\ensuremath{\Gamma}}$ and $\mathrm{M}$ points for ${\mathrm{EuMg}}_{2}{\mathrm{Sb}}_{2}$.