The ban means Kimmich will miss Bayern's match at Borussia Dortmund on Saturday and the home game with promoted Heidenheim next week.
Germany international Kimmich was shown a straight red card when he failed to control a pass from his own goalkeeper Manuel Neuer (37) and then pulled down Marwin Mehlem (26) at the edge of the box.
Darmstadt then had two players dismissed before the hosts scored eight times after the break.
Champions Bayern are in second place on 23 points, two behind leaders Bayer Leverkusen. Dortmund are fourth on 21.