Higher-order topological (HOT) states, hosting topologically protected modes on lower-dimensional boundaries, such as hinges and corners, have recently extended the realm of the static topological phases. Here we demonstrate the possibility of realizing a two-dimensional Floquet second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment QxyFlq=0.5, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold (C4) and time-reversal (T) symmetry breaking Dirac mass perturbation. Furthermore, we show that QxyFlq becomes independent of the choice of origin as the system approaches the thermodynamic limit. We also analyze the dynamics of a corner mode after a sudden quench, when the C4 and T symmetry breaking perturbation is switched off, and find that the corresponding survival probability displays periodic appearances of complete, partial and no revival for long time, encoding the signature of corner modes in a QSHI. Our protocol is sufficiently general to explore the territory of dynamical HOT phases in insulators and gapless systems.