Single crystals of pure and cupric ion (Cu(II))-doped magnesium rubidium sulfate hexahydrate (MRSH) were prepared by slow evaporation of saturated solution technique (SEST) and the influence of dopant Cu(II) on the MRSH crystals has been investigated. Incorporation of Cu(II) into the crystalline matrix was confirmed by energy dispersive spectroscopy (EDS) and electron paramagnetic resonance (EPR) spectroscopy. Thermogravimetric (TG) analysis of the doped sample reveals the faster rate of degradation. EPR spectrum of the MRSH both at room temperature and at 77 K indicates the presence of Cu(II) in the interstitial position. The grown crystals were also characterized by UV–VIS and IR spectroscopy. The surface morphology of the doped sample studied by scanning electron microscopy (SEM) indicates different morphology at various magnifications. The non-linear optical (NLO) property measured using second harmonic generation (SHG) efficiency test reveals that the non-linearity is not facilitated by doping of Cu(II).