Early diagnosis of disease can lead to improved health outcomes, including higher survival rates and lower treatment costs. With the massive amount of information available in electronic health records (EHRs), there is great potential to use machine learning (ML) methods to model disease progression aimed at early prediction of disease onset and other outcomes. In this work, we employ recent innovations in neural ODEs combined with rich semantic embeddings of clinical codes to harness the full temporal information of EHRs. We propose ICE-NODE (Integration of Clinical Embeddings with Neural Ordinary Differential Equations), an architecture that temporally integrates embeddings of clinical codes and neural ODEs to learn and predict patient trajectories in EHRs. We apply our method to the publicly available MIMIC-III and MIMIC-IV datasets, and we find improved prediction results compared to state-of-the-art methods, specifically for clinical codes that are not frequently observed in EHRs. We also show that ICE-NODE is more competent at predicting certain medical conditions, like acute renal failure, pulmonary heart disease and birth-related problems, where the full temporal information could provide important information. Furthermore, ICE-NODE is also able to produce patient risk trajectories over time that can be exploited for further detailed predictions of disease evolution.