  We embed $\mu-\tau$ reflection symmetry into the minimal seesaw formalism,
where two right-handed neutrinos are added to the Standard Model of particle
physics. Assuming that both the left- and right-handed neutrino fields
transform under $\mu-\tau$ reflection symmetry, we obtain the required forms of
the neutrino Dirac mass matrix and the Majorana mass matrix for the
right-handed neutrinos. To investigate the neutrino phenomenology at low
energies, we first consider the breaking of $\mu-\tau$ reflection symmetry due
to the renormalization group running, and then systematically study various
breaking schemes by introducing explicit breaking terms at high energies.
