We observe a density-dependent collective suppression of optical pumping between the hyperfine ground states in an array of submicrometer-sized clouds of dense and cold rubidium atoms. The suppressed Raman transition rate can be explained by strong resonant dipole-dipole interactions that are enhanced by increasing atom density, and are already significant at densities of ﰀ0.1k3, where k denotes the resonance wave number. The observations are consistent with stochastic electrodynamics simulations that incorporate the effects of population transfer via internal atomic levels embedded in a coupled-dipole model.