The age‐related loss of skeletal muscle mass and function (sarcopenia) is a consistent hallmark of ageing. Apoptosis plays an important role in muscle atrophy, and the intent of this study was to specify whether apoptosis is restricted to myofibre nuclei (myonuclei) or occurs in satellite cells or stromal cells of extracellular matrix (ECM). Sarcopenia in mouse gastrocnemius muscle was characterized by myofibre atrophy, oxidative type grouping, delocalization of myonuclei and ECM fibrosis. Terminal deoxynucleotidyl transferase‐mediated dUTP nick end‐labelling (TUNEL) indicated a sharp rise in apoptosis during ageing. TUNEL coupled with immunostaining for dystrophin, paired box protein‐7 (Pax7) or laminin‐2α, respectively, was used to identify apoptosis in myonuclei, satellite cells and stromal cells. In adult muscle, apoptosis was not detected in myofibres, but was restricted to stromal cells. Moreover, the age‐related rise in apoptotic nuclei was essentially due to stromal cells. Myofibre‐associated apoptosis nevertheless occurred in old muscle, but represented < 20% of the total muscle apoptosis. Specifically, apoptosis in old muscle affected a small proportion (0.8%) of the myonuclei, but a large part (46%) of the Pax7⁺ satellite cells. TUNEL coupled with CD31 immunostaining further attributed stromal apoptosis to capillary endothelial cells. Age‐dependent rise in apoptotic capillary endothelial cells was concomitant with altered levels of key angiogenic regulators, perlecan and a perlecan domain V (endorepellin) proteolytic product. Collectively, our results indicate that sarcopenia is associated with apoptosis of satellite cells and impairment of capillary functions, which is likely to contribute to the decline in muscle mass and functionality during ageing.