The performance of physical layer secrecy approach in non-orthogonal multiple access (NOMA)-enabled heterogeneous networks (HetNets) is analyzed in this paper. A $K$-tier multi-cell HetNet is considered, comprising NOMA adopted in all tiers. The base stations, legitimate users (in a two-user NOMA setup), and passive eavesdroppers, all with single-antenna, are randomly distributed. Assuming independent Poisson point processes for node distribution, stochastic geometry approaches are exploited to characterize the ergodic secrecy rate. A lower bound on the ergodic secrecy rate along with closed-form expressions for the lower bound on the ergodic rates of the legitimate users in a special case are derived. Moreover, simpler expressions for the ergodic secrecy rate are obtained in the interference-limited regime with vanishing noise variance. The effect of multi-tier technology, NOMA, and physical layer secrecy are investigated using numerical results. The results reveal that applying HetNet to a secure multi-cell NOMA system improves the spectrum efficiency performance.