The study of the interaction of nanoparticles (NPs) with proteins is of great importance due to its relevance in several fields including nano-biosafety, nano-bioscience, nano-biomedicine, and nano-biotechnology. However, the concentration dependency of NP–protein interactions and the effects on protein structure and function remain to be explored. Herein, we report the effect of concentration of iron oxide NPs, including Fe3O4 and Fe3O4 incorporated with arginine (Fe3O4@Arg), on the stability of hen egg white lysozyme (HEWL) (EC 220.127.116.11) used as a model protein. The NPs were synthesized and characterized using various methods, including Fourier transform infrared (FT-IR), transmission electron microscopy (TEM), scanning electron microscopy (SEM), vibrating sample magnetometer (VSM), dynamic light scattering (DLS), and X-ray diffraction (XRD). Subsequently, an attempt was made to explore the influence of the two types of NPs on the structure and stability of HEWL using fluorescence and circular dichroism (CD) spectroscopies. Moreover, functional stability analysis was performed by monitoring the remaining enzymatic activity of HEWL. Dual concentration dependent (DCD) effect of NPs on HEWL was observed, in which concentration threshold shift between two opposing effects, that is structure-making and structure-breaking, were determined to be 12.86 mg per μmol protein and 3.6 mg per μmol protein for Fe3O4 and Fe3O4@Arg, respectively. Kosmotropic-like and inversely chaotropic-like effects of NPs on HEWL are reported at lower and higher NPs/protein ratios, respectively. Accordingly, protein folding, helicity, and half-life were improved at a low concentration of NPs. The NPs act on HEWL structure and stability presumably through electrostatic adsorption on NPs, which, in turn, influences the structure and dynamics of the hydration water shell surrounding the protein molecules in the aqueous solution of HEWL. Therefore, NPs can act on HEWL either as a friend or foe depending on their concentration.