We calculate the dc magnetization of a three-dimensional array of weakly Josephson-coupled superconducting grains whose dimensions are of the order of the intragranular weak-field penetration depth. Because of significant flux penetration into small grains, the initial slope of the magnetization versus applied field not only is smaller than that for very large grains of the same shape, but also decreases with increasing temperature and vanishes at the critical temperature. The same behavior is expected for the ac susceptibility versus increasing temperature in a sample cooled in zero field. The dc magnetization is found to exhibit a corresponding size-dependent suppression for all fields up to the upper critical field.