The structure of the neutron-rich sodium isotopes {sup 31,32,33}Na was investigated by means of in-beam gamma-ray spectroscopy following one-neutron knockout and inelastic scattering of radioactive beams provided by the RIKEN Radioactive Ion Beam Factory. The secondary beams were selected and separated by the fragment separator BigRIPS and incident at approx =240 MeV/nucleon on a natural carbon (secondary) target, which was surrounded by the DALI2 array to detect coincident de-excitation gamma rays. Scattered particles were identified by the spectrometer ZeroDegree. In {sup 31}Na, a new decay gamma ray was observed in coincidence with the known (5/2{sub 1}{sup +})->3/2{sub g.s.}{sup (+)} transition, while for {sup 32,33}Na excited states are reported for the first time. From a comparison to state-of-the-art shell-model calculations it is concluded that the newly observed excited state in {sup 31}Na belongs to a rotational band formed by a 2p2h intruder configuration within the 'Island of Inversion.'