Three polycrystalline MgFe2O4 ferrite nanoparticles; MF1, MF2, and MF3 were prepared by the sot gel autocombustion method. The structural, elastic, and magnetic properties were studied using X-ray powder diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR) measurements, and vibrating sample magnetometer (VSM). X-ray powder diffraction patterns confirm the formation of the pure cubic spinet phase. The particle size (D) was determined and found to be 3 nm, 37 nm, and 48 nm for MF1, MF2, and MF3, respectively. The elastic parameters showed a weak dependence on the particle size. The magnetic hysteresis loops indicated that the saturation magnetization (M-s) and coercivity (H-e) decreased with decreasing the particle size (D). The values of the coercivity are size-dependent, which suggests that the prepared samples have a single magnetic domain structure. The temperature dependence of the magnetic parameters was investigated for the samples, whereas, the saturation magnetization and coercivity were increased with decreasing temperature.