The EU General Data Protection Regulation (GDPR) mandates the principle of data minimization, which requires that only data necessary to fulfill a certain purpose be collected. However, it can often be difficult to determine the minimal amount of data required, especially in complex machine learning models such as neural networks. We present a first-of-a-kind method to reduce the amount of personal data needed to perform predictions with a machine learning model, by removing or generalizing some of the input features. Our method makes use of the knowledge encoded within the model to produce a generalization that has little to no impact on its accuracy. This enables the creators and users of machine learning models to acheive data minimization, in a provable manner.