There has always been birth, so it is no surprise that the origins of the word midwife can be found as early as the Middle Ages. In Old High German they said “Hev(i)anna”. That meant something like “Hebe-Ahnin”. The midwife was an ancestor or grandmother who picked up the newborn from the ground.
In Middle High German, “Hev(i)anna” was reinterpreted as “Hebe-Amme” – this was the direct predecessor of the modern word. Incidentally, today's midwife is one of the few so-called generic feminines, words that do not have a masculine form. As a compromise, the male titles obstetrician and maternity nurse were introduced.