Music generation is pivotal in multimedia, aiding creation and lowering the creative threshold. It focuses on generating music with clear vocals and harmonious accompaniment based on lyrics, combining high artistic creativity with technical challenges. The music codec is an important bridging component in large language model-based music generation, connecting language models with the generated music. However, existing neural codecs typically require token rates exceeding 50 Hz to achieve acceptable music quality, resulting in a context length that surpasses 12,000 tokens for a 4-minute song—a scale that is computationally demanding. This highlights the need for high-compression, high-fidelity music codecs that can reconstruct both vocals and accompaniment with high quality at low frame rates and bitrates, thereby better assisting music generation. To address this, we introduce MuCodec, designed for high-quality music reconstruction at ultra-low bitrates, facilitating more efficient music generation. MuCodec employs a two-stage training method, enabling its encoder, MuEncoder, to extract semantic and acoustic features in a unified representation. These features are discretized using residual vector quantization and converted into Mel-VAE features through flow matching, with reconstruction quality improved by representation alignment during training. The Mel-VAE features are then reconstructed into music using a pre-trained Mel-VAE decoder and HiFi-GAN. To the best of our knowledge, MuCodec is the first codec capable of reconstructing 48kHz stereo music at an ultra-low bitrate of 0.35 kbps (25 Hz), achieving state-of-the-art performance in both subjective and objective evaluations, and can more effectively support music generation.