The optical absorption spectra of two-dimensional (2D) arrays of spatially dispersive metallic nanoparticles is examined. The corresponding non-local dielectric function of the spheres is provided by (a) the hydrodynamic approximation and (b) the Lindhard theory. More specifically, it is shown that the adoption of either types of non-local dielectric functions (hydrodynamic or Lindhard-type) for dilute 2D arrays of spheres does not alter the structure of the optical absorption spectrum but leads to a blue-shift of all its distinct features. This effect becomes more prominent as the radius of the nanoparticles decreases. However, for a close-packed arrangement of spheres, a non-local dielectric function provides a significantly different optical spectrum than the local one, due to the dominant role of near-field effects, which strongly depend on the choice of the dielectric function of the metal.