Motivated by the successful preparation of MoSi₂N₄ monolayers in the last year [Y.-L. Hong et al., Science, 2020, 369, 670–674], we investigate the structural, electronic and optical properties of the MoS₂/MoSi₂N₄ heterostructure (HTS). The phonon dispersion and the binding energy calculations refer to the stability of the HTS. The heterostructure has an indirect bandgap of 1.26 (1.84) eV using PBE (HSE06) which is smaller than the corresponding value of MoSi₂N₄ and MoS₂ monolayers. We find that the work function of the MoS₂/MoSi₂N₄ HTS is smaller than the corresponding value of its individual monolayers. The heterostructure structure can enhance the absorption of light spectra not only in the ultraviolet region but also in the visible region as compared to MoSi₂N₄ and MoS₂ monolayers. The refractive index behaviour of the HTS can be described as the cumulative effect which is well described in terms of a combination of the individual effects (the refractive index of MoSi₂N₄ and MoS₂ monolayers).