"form-fitting undergarment to support a woman's breasts," by 1902, a euphemistic borrowing in the garment trade, from French brassière "child's chemise; shoulder strap" (17c.), from Old French braciere "arm guard" (14c.), from bras "an arm," from Latin bracchium "an arm," from Greek brakhion "an arm" (see brachio-). The French word was used 18c. in the sense "woman's underbodice."
<a href="https://www.etymonline.com/word/bra">Etymology of bra by etymonline</a>
Harper, D. (n.d.). Etymology of bra. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/bra