High-precision mass measurements of neutron-rich 57−66 Mn and 61−63 Fe isotopes are reported. The new mass surface shows no shell closure at N = 40. In contrast, there is an increase of the two-neutron separation energy at N = 38. This behavior is consistent with the onset of collectivity due to the occupation of intruder states from higher orbits, in analogy with the well known "island of inversion" around N = 20. Our results indicate that the neutron-rich Mn isotopes, starting from 63 Mn, are most likely within the new island of inversion. From the new mass surface, we evaluate the empirical proton-neutron interaction and the pairing gap, both playing a significant role in the structural changes in this region.