In this paper, a chance-constrained (CC) framework is developed to manage the voltage control problem of medium-voltage (MV) distribution systems subject to model uncertainty. Such epistemic uncertainties are inherent in distribution system analyses given that an exact model of the network components is not available. In this context, relying on the simplified deterministic models can lead to insufficient control decisions. The CC-based voltage control framework is proposed to tackle this issue while being able to control the desired protection level against model uncertainties. The voltage control task disregarding the model uncertainties is firstly formulated as a linear optimization problem. Then, model uncertainty impacts on the above linear optimization problem are evaluated. This analysis defines that the voltage control problem subject to model uncertainties should be modelled with a joint CC formulation. The latter is accordingly relaxed to individual CC optimizations using the proposed methods. The performance of proposed CC voltage control methods is finally tested in comparison with that of the robust optimization. Simulation results confirm the accuracy of confidence level expected from the proposed CC voltage control formulations. The proposed technique allows the system operators to tune the confidence level parameter such that a tradeoff between operation costs and conservatism level is attained.