  We study the slow crossing of non-equilibrium quantum phase transitions in
periodically-driven systems. We explicitly consider a spin chain with a uniform
time-dependent magnetic field and focus on the Floquet state that is
adiabatically connected to the ground state of the static model. We find that
this {\it Floquet ground state} undergoes a series of quantum phase transitions
characterized by a non-trivial topology. To dinamically probe these
transitions, we propose to start with a large driving frequency and slowly
decrease it as a function of time. Combining analytical and numerical methods,
we uncover a Kibble-Zurek scaling that persists in the presence of moderate
interactions. This scaling can be used to experimentally demonstrate
non-equilibrium transitions that cannot be otherwise observed.
