The multiple images observed in galaxy cluster Abell 1689 provide strong constraints not only on the mass distribution of the cluster but also on the ensemble properties of the cluster galaxies. Using parametric strong lensing models for the cluster, and by assuming well motivated scaling laws between the truncation radius s and the velocity dispersion sigma of a cluster galaxy we are able to derive sizes of the dark matter halos of cluster galaxies. For the scaling law expected for galaxies in the cluster environment (s propto sigma), we obtain s = 64^{+15}_{-14} (sigma / 220 km/s) kpc. For the scaling law used for galaxies in the field with s propto sigma^2 we find s = 66^{+18}_{-16} (sigma / 220 km/s)^2 kpc. Compared to halos of field galaxies, the cluster galaxy halos in Abell 1689 are strongly truncated. ; Comment: 12 pages, 4 figures. Accepted for publication in the ApJ