Satellite cells are muscle stem cells required for muscle regeneration upon damage. Of note, satellite cells are bipotent and have the capacity to differentiate not only into skeletal myocytes, but also into brown adipocytes. Epigenetic mechanisms regulating fate decision and differentiation of satellite cells during muscle regeneration are not yet fully understood. Here, we show that elevated levels of lysine-specific demethylase 1 (Kdm1a, also known as Lsd1) have a beneficial effect on muscle regeneration and recovery after injury, since Lsd1 directly regulates key myogenic transcription factor genes. Importantly, selective Lsd1 ablation or inhibition in Pax7-positive satellite cells, not only delays muscle regeneration, but changes cell fate towards brown adipocytes. Lsd1 prevents brown adipocyte differentiation of satellite cells by repressing expression of the novel pro-adipogenic transcription factor Glis1. Together, downregulation of Glis1 and upregulation of the muscle-specific transcription program ensure physiological muscle regeneration.