  We present a direct spectroscopic observation of a shallow hydrogen-like
muonium state in SrTiO$_3$ which confirms the theoretical prediction that
interstitial hydrogen may act as a shallow donor in this material. The
formation of this muonium state is temperature dependent and appears below
$\sim 70$ K. From the temperature dependence we estimate an activation energy
of $\sim 50$ meV in the bulk and $\sim 23$ meV near the free surface. The field
and directional dependence of the muonium precession frequencies further
supports the shallow impurity state with a rare example of a fully anisotropic
hyperfine tensor. From these measurements we determine the strength of the
hyperfine interaction and propose that the muon occupies an interstitial site
near the face of the oxygen octahedron in SrTiO$_3$. The observed shallow donor
state provides new insight for tailoring the electronic and optical properties
of SrTiO$_{3}$-based oxide interface systems.
