  Short-distance QCD is employed to calculate the $J/\psi$ survival probability
in an equilibrating parton gas, whose evolution is governed by a set of master
rate equations. Partons in the early stage of high-energy nuclear collisions
may initially not be in equilibrium, but their average transverse momentum is
sufficiently high to break up a $Q\bar{Q}$ bound state. Such a break-up during
the evolution of the parton gas is shown to cause a substantial $J/\psi$
suppression at both RHIC and LHC energies, using realistic estimates of the
initial parton densities. The transverse momentum dependence of the suppression
is also shown to be sensitive to the initial conditions and the evolution
history of the parton plasma.
