Electronic health record (EHR) data has emerged as a valuable resource for analyzing patient health status. However, the prevalence of missing data in EHR poses significant challenges to existing methods, leading to spurious correlations and suboptimal predictions. While various imputation techniques have been developed to address this issue, they often obsess difficult-to-interpolate details and may introduce additional noise when making clinical predictions. To tackle this problem, we propose SMART, a Self-Supervised Missing-Aware RepresenTation Learning approach for patient health status prediction, which encodes missing information via missing-aware temporal and variable attentions and learns to impute missing values through a novel self-supervised pre-training approach which reconstructs missing data representations in the latent space rather than in input space as usual. By adopting elaborated attentions and focusing on learning higher-order representations, SMART promotes better generalization and robustness to missing data. We validate the effectiveness of SMART through extensive experiments on six EHR tasks, demonstrating its superiority over state-of-the-art methods.