1590s, "money box;" also "money in hand, coin," from Middle French caisse "money box" (16c.), from Provençal caissa or Italian cassa, from Latin capsa "box" (see case (n.2)); originally the money box, but the secondary sense of the money in it became sole meaning 18c. Cash crop is attested from 1831; cash flow from 1954; the mechanical cash register from 1878.
Like many financial terms in English (bankrupt, etc.), ultimately from Italian. Not related to (but influencing the form of) the colonial British cash "Indian monetary system, Chinese coin, etc.," which is from Tamil kasu, Sanskrit karsha, Sinhalese