Second-order phase transitions are governed by spontaneous symmetry breaking, which yield collective excitations with a gapless spectrum called Nambu-Goldstone (NG) modes. While NG modes in conservative systems are propagating excitations, non-equilibrium phase transitions have been predicted to feature a diffusive NG mode. We present the first experimental evidence of a diffusive NG mode in a non-equilibrium Bose-Einstein condensate of microcavity polaritons. The NG mode is observed as a spectral narrowing in the spectroscopic response of the condensate. Additionally, explicitly breaking the symmetry causes the opening of a gap in the spectrum and the disappearance of the NG mode. Our observations confirm the diffusive dynamics of the NG mode of non-equilibrium phase transitions and establish a promising framework to investigate fundamental questions in statistical mechanics.