This study investigates the risks of exposing confidential chemical structures when machine learning models trained on these structures are made publicly available. We use membership inference attacks, a common method to assess privacy that is largely unexplored in the context of drug discovery, to examine neural networks for molecular property prediction in a black-box setting. Our results reveal significant privacy risks across all evaluated datasets and neural network architectures. Combining multiple attacks increases these risks. Molecules from minority classes, often the most valuable in drug discovery, are particularly vulnerable. We also found that representing molecules as graphs and using message-passing neural networks may mitigate these risks. We provide a framework to assess privacy risks of classification models and molecular representations. Our findings highlight the need for careful consideration when sharing neural networks trained on proprietary chemical structures, informing organisations and researchers about the trade-offs between data confidentiality and model openness.