A novel signaling design for secure transmission over two-user multiple-input multiple-output non-orthogonal multiple access channel using deep neural networks (DNNs) is proposed. The goal of the DNN is to form the covariance matrix of users' signals such that the message of each user is transmitted reliably while being confidential from its counterpart. The proposed DNN linearly precodes each user's signal before superimposing them and achieves near-optimal performance with significantly lower run time. Simulation results show that the proposed models reach about 98% of the secrecy capacity rates. The spectral efficiency of the DNN precoder is much higher than that of existing analytical linear precoders--e.g., generalized singular value decomposition--and its on-the-fly complexity is several times less than the existing iterative methods.