We propose an encrypted set-theoretic model predictive control (ST-MPC) strategy for cloud-based networked control systems. In particular, we consider a scenario where the plant is subject to state and input constraints, and a curious but honest cloud provider is available to implement the control logic remotely. We address the inherent privacy issue by jointly using an additive homomorphic cryptosystem and a modified version of the ST-MPC algorithm, which is tailored to run on encrypted data. We show that, by leveraging a family of zonotopic inner approximations of robust one-step controllable sets and a half-space projection algorithm, we can design the unavoidable computational load on the smart actuator’s side to be real-time affordable by the available hardware compared to other existing solutions. A simulation experiment, considering a two-tank water system, is presented to verify the effectiveness of the proposed approach.