A form of programmed cell death induced by external or internal signals that trigger the activity of proteolytic caspases, whose actions dismantle a muscle cell and result in its death. A muscle cell is a mature contractile cell, commonly known as a myocyte, that forms one of three kinds of muscle. [ http://purl.obolibrary.org/obo/CL_0000187 GOC:dph GOC:tb GOC:mtg_apoptosis ]