  We study the time-dependent circuit complexity of the periodically driven
transverse field Ising model using Nielsen's geometric approach. In the
high-frequency driving limit the system is known to exhibit non-equilibrium
phase transitions governed by the amplitude of the driving field. We
analytically compute the complexity in this regime and show that it clearly
distinguishes between the different phases, exhibiting a universal linear
behavior at early times. We also evaluate the time averaged complexity, provide
evidence of non-analytic behavior at the critical points, and discuss its
origin. Finally, we comment on the freezing of quantum dynamics at specific
configurations and on the use of complexity as a new tool to understand quantum
phase transitions in Floquet systems.
