Display Screen or Portion Thereof with Animated Icon

FIG. 1 is a front view of the first image in a sequence for a display screen or portion thereof with animated icon; FIG. 2 is the second image thereof; FIG. 3 is the third image thereof; FIG. 4 is the fourth image thereof; FIG. 5 is the fifth image thereof; and, FIG. 6 is the sixth image thereof. The appearance of the transitional image sequentially transitions between the images shown in FIGS. 1 - 6 . The process or period in with one image transitions to another image forms no part of the claimed design. The outermost broken line presents a display screen or portion thereof and forms no part of the claimed design.