In this work, the effect of uniaxial strain on electronic and thermoelectric properties of magnesium silicide using density functional theory (DFT) and Boltzmann transport equations has been studied. We have found that the value of band gap increases with tensile strain and decreases with compressive strain. The variations of electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and power factor with temperatures have been calculated. The Seebeck coefficient and power factor are observed to be modified strongly with strain. The value of power factor is found to be higher in comparison with the unstrained structure at 2% tensile strain. We have also calculated phonon dispersion, phonon density of states, specific heat at constant volume, and lattice thermal conductivity of material under uniaxial strain. The phonon properties and lattice thermal conductivity of Mg_{2}Si under uniaxial strain have been explored first time in this report.