The structural, electronic, elastic, dynamic and optical properties of the ternary chalcopyrite compound MgGeSb2 were studied by using the density functional theory (DFT) framework for different exchange-correlation functionals. The obtained equilibrium structural parameters are in good agreement with the available theoretical result. After considering the electronic band structure and electronic density of states (DOS) calculation; this compound is a semiconductor as suggested in the previous work. However; all considered functionals underestimate considerably the electronic band gap energies compared with the experimental results. We have predicted single-crystal elastic constants and related properties such as Young's modulus, Poisson ratio, shear modulus and bulk modulus. Optical properties such as the dielectric function, refractive index, extinction index have been calculated in the range of 0-20 eV. The obtained results can facilitate an assessment of possible applications of MgGeSb2.