We investigate relative stability, structural properties and electronic structure of various modulated martensites of the magnetic shape memory alloy Mn$_{2}$NiGa by means of density functional theory. We observe that the instability in the high-temperature cubic structure first drives the system to a structure where modulation shuffles with a period of six atomic planes are taken into account. The driving mechanism for this instability is found to be the nesting of the minority band Fermi surface, in a similar way as established for the prototype system Ni$_{2}$MnGa. In agreement with experiments, we find 14M modulated structures with orthorhombic and monoclinic symmetries having energies lower than other modulated phases with same symmetry. In addition, we also find energetically favourable 10M modulated structures which have not been observed experimentally for this system yet. The relative stability of various martensites is explained in terms of changes in the electronic structures near the Fermi level, affected mostly by the hybridisation of Ni and Mn states. Our results indicate that the maximum achievable magnetic field-induced strain in Mn$_{2}$NiGa would be larger than in Ni$_{2}$MnGa. However, the energy costs for creating nanoscale adaptive twin boundaries are found to be one order of magnitude higher than that in Ni$_{2}$MnGa.
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