Recent improvements in neural audio codec (NAC) models have generated interest in adopting pre-trained codecs for a variety of speech processing applications to take advantage of the efficiencies gained from high compression, but these have yet been applied to the speech separation (SS) task. SS can benefit from high compression because the compute required for traditional SS models makes them impractical for many edge computing use cases. However, SS is a waveform-masking task where compression tends to introduce distortions that severely impact performance. Here we propose a novel task of Audio Codec-based SS, where SS is performed within the embedding space of a NAC, and propose a new model, Codecformer, to address this task. At inference, Codecformer achieves a 52x reduction in MAC while producing separation performance comparable to a cloud deployment of Sepformer. This method charts a new direction for performing efficient SS in practical scenarios.