Deep learning is revolutionizing predictive healthcare, including recommending medications to patients with complex health conditions. Existing approaches focus on predicting all medications for the current visit, which often overlaps with medications from previous visits. A more clinically relevant task is to identify medication changes. In this paper, we propose a new recurrent residual networks, named MICRON, for medication change prediction. MICRON takes the changes in patient health records as input and learns to update a hid- den medication vector and the medication set recurrently with a reconstruction design. The medication vector is like the memory cell that encodes longitudinal information of medications. Unlike traditional methods that require the entire patient history for prediction, MICRON has a residual-based inference that allows for sequential updating based only on new patient features (e.g., new diagnoses in the recent visit), which is efficient. We evaluated MICRON on real inpatient and outpatient datasets. MICRON achieves 3.5% and 7.8% relative improvements over the best baseline in F1 score, respectively. MICRON also requires fewer parameters, which significantly reduces the training time to 38.3s per epoch with 1.5× speed-up.