Structural model uncertainty is prevalent in control design and arises from incomplete knowledge of the system or the existence of different modes of dynamic behavior, such as those arising from system faults and malfunctions. This paper addresses control of stochastic nonlinear systems using model predictive control, or MPC, under structural model uncertainty. Inspired by dual control, the MPC strategy with active learning presented here can probe the uncertain system to select, among a set of candidates, the model that best describes the observed closed-loop system data. The proposed controller involves online model selection based on estimation of the model-hypothesis probabilities and minimization of a computationally tractable measure of the predicted Bayes risk of selection error. The performance of the proposed approach is compared to that of nominal MPC with no learning, MPC with passive learning, and a robust MPC approach that systematically accounts for structural model uncertainty but has no learning mechanism. Simulation results on a nonlinear bioreactor demonstrate that active learning can have significant advantages in maintaining adequate control performance in the presence of structural uncertainty. Active learning can be particularly beneficial for improving online model discrimination and active fault diagnosis under closed-loop control. (C) 2019 Elsevier Ltd. All rights reserved.