"long, narrow ulcer," late 14c., from Latin fistula "a pipe; ulcer," which is of uncertain origin. Related: Fistular; fistulous (Latin fistulosus "full of holes; tubular").
No certain etymology. The best comparison seems to be with festuca "stalk, straw" and maybe ferula "giant fennel" (if from *fesula): the forms of a "pipe" and a "stalk" are similar. The vacillation between fest- and fist- occurs within festuca itself, and might be dialectal, or allophonic within Latin. [de Vaan]