Any apoptotic process in a motor neuron, an efferent neuron that passes from the central nervous system or a ganglion toward or to a muscle and conducts an impulse that causes movement. [ GOC:BHF http://purl.obolibrary.org/obo/CL_0000100 GOC:mtg_apoptosis http://www.ncbi.nlm.nih.gov/pubmed/14523086 ]