We investigate an orderly study of the adiabatic potential energy curves for 29 and 30 low-lying 2s+1Λ+/− electronic states of the molecules MgLi and MgNa, respectively. The calculation has been done by using the complete active space self-consistent field followed by multi-reference configuration interaction with Davidson correction. For the investigated electronic states, the static and transition dipole moment curves are calculated along with the Einstein coefficients, the emission oscillator strength, the spontaneous radiative lifetime, the line strength, the classical radiative decay rate of the single-electron oscillator, the spectroscopic constants (Te, ωe, ωexe, Be, Re), and the equilibrium dissociation energy De. By means of the canonical functions approach, the ro-vibrational constants Ev, Bv, Dv, and the abscissas of the turning points, Rmin and Rmax, have been calculated for the considered electronic states up to the vibrational level v = 79. The Franck–Condon factors have been calculated and plotted for the transition between the low-lying electronic states of the two considered molecules. A good agreement is revealed between our calculated values and those available in the literature. Fifty new electronic states are investigated in the present work for the first time.