In this paper, we apply covert communications to reconfigurable intelligent surface (RIS)-assisted non-orthogonal multiple access (NOMA) networks, where a legitimate transmitter sends messages to a pair of legitimate users while a warden aims to detect whether the legitimate transmission exists. We can hide the existence of the strong user's transmission from a warden by exploiting the nature of NOMA, i.e., allocating less power to the strong user, and we use a jammer to further hide that existence. Correspondingly, we analyze the system performance and obtain the closed-form expression for the minimum detection error probability. Simulation results validate the correctness of our analysis and demonstrate the covertness of the proposed scheme.