A challenge in aircraft design optimization is the presence of non-computable, so-called hidden, constraints that do not return a value in certain regions of the design space. In this paper, we present a novel method to handle hidden constraints in aircraft conceptual design using Bayesian optimization. The method entails modifying a portion of the acquisition function of a Bayesian optimization formulation using supervised machine learning classifiers. The proposed approach reduces the effect of classifiers on exploration, therefore allowing the optimization algorithm to consider regions of the design space where previous information is not available. In addition, we consider different classifiers for handling hidden constraints. We demonstrate the proposed method using two simulation-based aircraft design optimization problems related to landing gear sizing and aircraft performance. The obtained results show an improvement of the objective function with fewer function evaluations.