We compute the isometry group for the curved momentum spaces compatible with k-Minkowski. Momentum spaces are associated to the non degenerated orbits of a 5D representation of the group manifold AN3 generated by the k-Minkowski algebra an3. Each inequivalent momentum space belongs to one of three classes (space,light, or
time-like), depending on the nature of the fiducial 5-dimensional vector used to construct the orbit. We compute the isometry group of each one of these momentum spaces as the Inönü-Wigner contraction of the global symmetry group of the embedding 5D space with respect to the stabilizer subgroup of the corresponding fiducial vector.