Old English midhrif "diaphragm of a human or animal," from mid "mid" (from PIE root *medhyo- "middle") + hrif "belly," from Proto-Germanic *hrefin (source also of Old High German href, Old Frisian hrif, -rith, -rede "belly"). Compare Old Frisian midrede "diaphragm." Watkins has this from PIE root *kwrep- "body, form, appearance;" Boutkan has it from *sker- (1) "to cut."
More or less obsolete after 18c. except in phrase to tickle (one's) midriff "to cause laughter;" the word revived 1941 in fashion usage for "portion of a woman's garment that covers the belly," as a euphemistic avoidance of belly; sense inverted and extended 1970 to a belly-baring style of women's top.