We derive a Margolus-Levitin-type bound on the minimal evolution time of an
arbitrarily driven open quantum system. We express this quantum speed limit
time in terms of the operator norm of the nonunitary generator of the
dynamics. We apply these results to the damped Jaynes-Cummings model and
demonstrate that the corresponding bound is tight. We further show that non-
Markovian effects can speed up quantum evolution and therefore lead to a
smaller quantum speed limit time.