Using a Drude-like model for the conduction electrons of Metal Nanoparticles (MNPs) assembled in a periodic two-dimensional (2D) array, considering dipole-dipole interactions of adjacent particles, an analytical expression is achieved for the MNP permittivity where the functionality of interaction term on the different geometric and physical parameters is evident. A numerical analysis is carried out for a gold NP array for two different sizes of NPs and two different host media of water and glass. It is shown that, interaction of NPs leads to a substantial increase in the extinction cross section, the red-shift of the Surface Plasmon Resonance (SPR) wavelength and decrease in the full width at half maximum (FWHM) of cross section. The absolute values of the real and imaginary parts of complex permittivity of each MNP decrease in comparison with the single particle case.