Any apoptotic process in an oligodendrocyte. Oligodendrocytes belong to a class of large neuroglial (macroglial) cells in the central nervous system, where they form the insulating myelin sheath of axons. [ GOC:yaf http://www.ncbi.nlm.nih.gov/pubmed/16723520 GOC:mtg_apoptosis http://purl.obolibrary.org/obo/CL_0000128 ]