We present the results of the measured shapes of 832 galaxies in 11 galaxy clusters at 1.0 < z < 1.4 from the GOGREEN survey. We measure the axis ratio (q), the ratio of the minor to the major axis, of the cluster galaxies from near-infrared Hubble Space Telescope imaging using Sersic profile fitting and compare them with a field sample. We find that the median q of both star-forming and quiescent galaxies in clusters increases with stellar mass, similar to the field. Comparing the axis ratio distributions between clusters and the field in four mass bins, the distributions for star-forming galaxies in clusters are consistent with those in the field. Conversely, the distributions for quiescent galaxies in the two environments are distinct, most remarkably in 10.1 <= log(M/M-circle dot)<10.5