"woman in domestic charge of a public institution, especially a hospital" When this word arrived in English in the 14th century, it referred simply to a "married woman" - especially one who had a dignified position in society. Then, in the 15th century, it narrowed in meaning, referring to a married woman who was especially knowledgeable about pregnancy and childbirth. By the end of the 16th century, it had begun to be used in its modern meaning, with no restriction to marriage; matrons can be, and often are, single. Shakespeare uses the word only in its original sense. When Timon expostulates to Alcibiades about matrons, he does not have hospitals in mind: "Strike me the counterfeit matron" (Timon of Athens, IV.iii.113).
Nor should we expect someone in a nurse's uniform to appear when we read the stage direction: "Enter...an ancient matron" (Cymberline, V.iv.30).
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin