Because Antarctic surface melt is mostly driven by local processes, its simulation necessitates high‐resolution regional climate models (RCMs). However, the current horizontal resolution of RCMs (≈25–30 km) is inadequate for capturing small‐scale melt processes. To address this limitation, we present SUPREME (SUPer‐REsolution‐based Melt Estimation over Antarctica), a deep learning method to downscale surface melt to 5.5 km resolution using a physically‐informed super‐resolution model. The physical information integrated into the model originates from observations tied to surface melt, specifically remote sensing‐derived albedo and elevation. These remote sensing data, in addition to a Regional Atmospheric Climate Model (RACMO) run at 27 km resolution, account for the diverse drivers of surface melt across Antarctica, facilitating effective generalization beyond the training region of the Antarctic Peninsula. A comparison of SUPREME with a dynamically downscaled RACMO run at 5.5 km over the Antarctic Peninsula shows high accuracy, with average yearly RMSE and bias of 5.5 mm w.e. yr−1 and 4.5 mm w.e. yr−1, respectively. Validation at five automatic weather stations reveals SUPREME's marked improvement with substantially lower average RMSE (81 mm w.e.) compared to RACMO 27 km (129 mm w.e.). Beyond the training region, SUPREME aligns more closely with remote sensing products associated with surface melt than super‐resolution models lacking physical constraints. While further validation of SUPREME is needed, our study highlights the potential of super‐resolution techniques with physical constraints for high‐resolution surface melt monitoring in Antarctica, providing insights into the impacts of localized melting on processes affecting ice shelf integrity such as hydrofracturing.