In this paper, we investigate the impact of phase noise on the secrecy performance of downlink massive MIMO systems in the presence of a passive multiple-antenna eavesdropper. Thereby, for the base station (BS) and the legitimate users, the effect of multiplicative phase noise is taken into account, whereas the eavesdropper is assumed to employ ideal hardware. We derive a lower bound for the ergodic secrecy rate of a given user when matched filter (MF) data precoding and artificial noise (AN) transmission are employed at the BS. Based on the derived analytical expression, we investigate the impact of the various system parameters on the secrecy rate. Our analytical and simulation results reveal that distributively deployed local oscillators (LOs) can achieve better performance as long as a sufficient amount of power is assigned for data transmission than one common LO for all BS antennas.