'Stigma' is Greek for 'a brand mark' — from 'stizein' (to prick). Literal mark turned figurative disgrace.
A mark of disgrace or discredit associated with a particular circumstance, quality, or person; historically, a mark burned or cut into the skin as a sign of shame.
From Latin 'stigma' (a mark, a brand), from Greek 'stigma' (a mark made by a pointed instrument, a tattoo, a brand), from 'stizein' (to prick, to puncture, to tattoo), from Proto-Indo-European '*steyg-' (to prick, to stick, to be sharp). In ancient Greece, slaves, criminals, and prisoners of war were branded with a 'stigma' — a literal mark burned into the skin. The figurative sense of 'a mark of shame or disgrace' developed in Latin and was well established
The 'stigmata' — wounds corresponding to those of Christ's crucifixion, appearing spontaneously on the bodies of certain devout people — use the same Greek word. Saint Francis of Assisi is traditionally regarded as the first stigmatic (1224). The plural 'stigmata' follows the Greek pattern, and this religious usage is the reason English preserved the unusual plural rather than simply saying 'stigmas.'