late 14c., matrone, "married woman," usually one of rank or social respectability and mature years (old enough to be the mother of a family, whether actually so or not), from Old French matrone "married woman; elderly lady; patroness; midwife," and directly from Latin mātrona "married woman, wife, matron," from māter (genitive mātris) "mother" (see mother (n.1)).
Also (15c.) "a married female saint." Sense of "female manager of a school, head nurse in a hospital, etc." is recorded by 1550s.