  Molecular outflows are expected to play a key role in galaxy evolution at
high redshift. To study the impact of outflows on star formation at the epoch
of reionization, we performed sensitive ALMA observations of OH 119 $\mu$m
toward J2054-0005, a luminous quasar at $z=6.04$. The OH line is detected and
exhibits a P-Cygni profile that can be fitted with a broad blue-shifted
absorption component, providing unambiguous evidence of an outflow, and an
emission component at near-systemic velocity. The mean and terminal outflow
velocities are estimated to be $v_\mathrm{out}\approx670~\mathrm{km~s}^{-1}$
and $1500~\mathrm{km~s}^{-1}$, respectively, making the molecular outflow in
this quasar one of the fastest at the epoch of reionization. The OH line is
marginally spatially resolved for the first time in a quasar at $z>6$,
revealing that the outflow extends over the central 2 kpc region. The mass
outflow rate is comparable to the star formation rate
($\dot{M}_\mathrm{out}/\mathrm{SFR}\sim2$), indicating rapid
($\sim10^7~\mathrm{yr}$) quenching of star formation. The mass outflow rate in
a sample star-forming galaxies and quasars at $4<z<6.4$ exhibits a positive
correlation with the total infrared luminosity, although the scatter is large.
Owing to the high outflow velocity, a large fraction (up to $\sim50\%$) of the
outflowing molecular gas may be able to escape from the host galaxy into the
intergalactic medium.
