Quantizing machine learning models has demonstrated its effectiveness in lowering memory and inference costs while maintaining performance levels comparable to the original models. In this work, we investigate the impact of quantization procedures on the privacy of data-driven models, specifically focusing on their vulnerability to membership inference attacks. We derive an asymptotic theoretical analysis of Membership Inference Security (MIS), characterizing the privacy implications of quantized algorithm weights against the most powerful (and possibly unknown) attacks. Building on these theoretical insights, we propose a novel methodology to empirically assess and rank the privacy levels of various quantization procedures. Using synthetic datasets, we demonstrate the effectiveness of our approach in assessing the MIS of different quantizers. Furthermore, we explore the trade-off between privacy and performance using real-world data and models in the context of molecular modeling.