  We consider an open system near a quantum critical point that is suddenly
moved towards the critical point. The bath-dominated diffusive non-equilibrium
dynamics after the quench is shown to follow scaling behavior, governed by a
critical exponent that emerges in addition to the known equilibrium critical
exponents. We determine this exponent and show that it describes universal
prethermalized coarsening dynamics of the order parameter in an intermediate
time regime. Implications of this quantum critical prethermalization are a
powerlaw rise of order and correlations after an initial collapse of the
equilibrium state and a crossover to thermalization that occurs arbitrarily
late for sufficiently shallow quenches.
