  We report the first observation of cyclotron resonance in the hidden-order
phase of ultra-clean URu$_2$Si$_2$ crystals, which allows the full
determination of angle-dependent electron-mass structure of the main
Fermi-surface sheets. We find an anomalous splitting of the sharpest resonance
line under in-plane magnetic-field rotation. This is most naturally explained
by the domain formation, which breaks the fourfold rotational symmetry of the
underlying tetragonal lattice. The results reveal the emergence of an in-plane
mass anisotropy with hot spots along the [110] direction, which can account for
the anisotropic in-plane magnetic susceptibility reported recently. This is
consistent with the `nematic' Fermi liquid state, in which itinerant electrons
have unidirectional correlations.
