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Can health conditions be inferred from an individual's mobility pattern? Existing research has discussed the relationship between individual physical activity/mobility and well-being, yet no systematic study has been done to investigate the predictability of fine-grained health conditions from mobility, largely due to the unavailability of data and unsatisfactory modelling techniques. Here, we present a large-scale longitudinal study, where we collect the health conditions of 747 individuals who visit a hospital and tracked their mobility for 2 months in Beijing, China. To facilitate fine-grained individual health condition sensing, we propose HealthWalks, an interpretable machine learning model that takes user location traces, the associated points of interest, and user social demographics as input, at the core of which a Deterministic Finite Automaton (DFA) model is proposed to auto-generate explainable features to capture useful signals. We evaluate the effectiveness of our proposed model, which achieves 40.29% in micro-F1 and 31.63% in Macro-F1 for the 8-class disease category prediction, and outperforms the best baseline by 22.84% in Micro-F1 and 31.79% in Macro-F1. In addition, deeper analysis based on the SHapley Additive exPlanations (SHAP) showcases that HealthWalks can derive meaningful insights with regard to the correlation between mobility and health conditions, which provide important research insights and design implications for mobile sensing and health informatics.