Massive multiple antenna systems in conjunction with millimeter (mmWave) communication have gained tremendous attention in the recent years owing to their high speed data delivery. However, security in these networks has been overlooked; thereby necessitating a comprehensive study. This paper analyzes the physical layer security performance of the downlink of a massive multiple-input multiple-output (MIMO)-based hybrid heterogeneous network (HetNet) where both mmWave and sub-6 GHz small cells coexist. Specifically, a tractable approach using stochastic geometry is proposed to analyze the secrecy outage probability, secrecy energy efficiency (SEE) and secrecy spectrum efficiency (SSE) of the hybrid HetNets. Our study further characterizes the impact of large antenna arrays, directional beamforming gains, transmit power, and cell density on the above mentioned secrecy performance measures. The results show that at low transmit power operation, the secrecy performance enhances for higher small cell density. It has also been observed that the higher directivity gains at mmWave cells lead to a drop in secrecy performance of the network; thus a tradeoff exists between better coverage or secrecy.