In this paper, the application of non-orthogonal multiple access (NOMA) into K-tier heterogeneous networks (HetNets) is investigated. A new promising transmission framework is proposed, in which massive multiple-input multiple-output (MIMO) is employed in macro cells and NOMA is adopted in small cells. For maximizing the biased average received power at mobile users, a massive MIMO and NOMA based user association scheme is developed. In an effort to evaluate the performance of the proposed framework, analytical expressions for the spectrum efficiency of each tier are derived using stochastic geometry. Simulation results are presented to verify the accuracy of the proposed analytical derivations and confirm that NOMA is capable of enhancing the spectrum efficiency of the network compared to the orthogonal multiple access (OMA) based HetNets.