  We investigate the Noether symmetries of the minimal surface Lagrangian for
four classes of metrics in G\"{o}del-type spacetimes. Then, calculating the
Noether symmetries for all classes, namely, classes I, II, III and IV, we
determine the conserved fields corresponding to each classes, allowing us to
derive a comprehensive characterization of the minimal surface equations for
G\"{o}del-type spacetimes.
