  We report on first direct observation of spontaneous fluctuations of
birefringence in glasses doped with rare-earth (RE) ions. The fluctuations were
observed in Nd$^{3+}$- and Yb$^{3+}$-doped glasses as polarization noise of the
laser beam transmitted through the sample in the region of the RE-ion
absorption. The noise was characterized by a flat (``white'') spectrum in the
range of frequencies up to 1 GHz and did not show any dependence on magnetic
field. The discovered polarization noise is interpreted in terms of structural
dynamics of glasses revealed at low temperatures and usually described in the
model of tunneling two-level systems (TLS). High sensitivity of the
polarization noise technique to this dynamics is related to small homogeneous
width of \textit{f-f} transitions of RE-ions in glasses and small spectral
width of the probe laser light. The discovered effect provides a new
experimental approach to studying low-temperature structural dynamics of
different disordered matrices and interactions of impurities with environment
in such media.
