Neurophysiological recordings such as electroencephalography (EEG) offer accessible and minimally invasive means of estimating physiological activity for applications in healthcare, diagnostic screening, and even immersive entertainment. However, these recordings yield high-dimensional, noisy time-series data that typically require extensive pre-processing and handcrafted feature extraction to reveal meaningful information. Recently, there has been a surge of interest in applying representation learning techniques from large pre-trained (foundation) models to effectively decode and interpret biosignals. We discuss the challenges posed for incorporating such methods and introduce BioCodec, an alternative representation learning framework inspired by neural codecs to capture low-level signal characteristics in the form of discrete tokens. Pre-trained on thousands of EEG hours, BioCodec shows efficacy across multiple downstream tasks, ranging from clinical diagnostic tasks and sleep physiology to decoding speech and motor imagery, particularly in low-resource settings. Additionally, we provide a qualitative analysis of codebook usage and estimate the spatial coherence of codebook embeddings from EEG connectivity. Notably, we also document the suitability of our method to other biosignal data, i.e., electromyographic (EMG) signals. Overall, the proposed approach provides a versatile solution for biosignal tokenization that performs competitively with state-of-the-art models. The source code and model checkpoints are shared.