Recent works have identified hybrid analog-digital processing as a cost-effective alternative to conventional full-digital processing in massive multiple-input multiple-output (MIMO) systems owing to the deployment of far less number of radio frequency (RF) chains. In this paper, we analyze the impact of oscillator phase noise on hybrid precoding in massive MIMO systems. Relying on the time division duplexing (TDD) operation, we design an efficient uplink (UL) channel estimation scheme suitable for the hybrid architecture by exploiting channel covariance matrices (CCMs) of sparse massive MIMO channels. Additionally, we employ a CCM aided RF precoder combined with regularized zero-forcing (RZF) precoding performed in the baseband. Subsequently, we derive the deterministic equivalent (DE) for the downlink (DL) signal-to-interference-plus-noise ratio (SINR), which visibly reveals the impact of phase noise on the performance of hybrid precoding in massive MIMO systems. Finally, we verify the analytical result and show the performance comparison of the proposed hybrid precoding scheme for different phase noise variances through Monte Carlo (MC) simulations.