Extracting balanced geostrophic motions (BM) from sea surface height (SSH) observations obtained by wide‐swath altimetry holds great significance in enhancing our understanding of oceanic dynamic processes at submesoscale wavelength. However, SSH observations derived from wide‐swath altimetry are characterized by high spatial resolution while relatively low temporal resolution, thereby posing challenges to extract the BM from a single SSH snapshot. To address this issue, this paper proposes a deep learning model called the BM‐UBM Network, which takes an instantaneous SSH snapshot as input and outputs the projection corresponding to the BM. Training experiments are conducted both in the Gulf Stream and South China Sea, and three metrics are considered to diagnose model's outputs. The favorable results highlight the potential capability of the BM‐UBM Network to process SSH measurements obtained by wide‐swath altimetry.