$MgIn_2Se_4 and MgIn_2Se_4 : Ni^{2+}$ single crystals were grown in the rhombohedral structure by the chemical transport reaction (C.T.R.) method using iodine as a transport agent. The optical absorption measured near the fundamental band edge showed that the optical energy band structure of these compounds had a direct band gap. The fundamental absorption band edge of these single crystals shift to a shorter wavelength region by decreasing temperature and the temperature dependence of the optical energy gaps in these compounds satisfy Varshni equation. The impurity optical absorption peaks due to nickel are observed in $MgIn_2Se_4 and MgIn_2Se_4 : Ni^{2+}$ single crystal. These impurity optical absorption peaks can be attributed to the electronic transitions between the split energy levels of $Ni_{2+}$ ions located at $T_d$ symmetry site of $MgIn_2Se_4$ host lattice. In the hotoluminescence spectrum of the single crystal at 10 K, a blue emission with a peak at 687nm and a green emission with a peak at 815nm for the $MgIn_2Se_4$ single crystal were observed.