We study the dynamics of entanglement asymmetry in periodically driven quantum systems. Using a periodically driven XY chain as a model for a driven integrable quantum system, we provide semi-analytic results for the behavior of the dynamics of the entanglement asymmetry, (\Delta S), as a function of the drive frequency. Our analysis identifies special drive frequencies at which the driven XY chain exhibits dynamic symmetry restoration and displays quantum Mpemba effect over a long timescale; we identify an emergent approximate symmetry in its Floquet Hamiltonian which plays a crucial role for realization of both these phenomena. We follow these results by numerical computation of (\Delta S) for the non-integrable driven Rydberg atom chain and obtain similar emergent-symmetry-induced symmetry restoration and quantum Mpemba effect in the prethermal regime for such a system. Finally, we provide an exact analytic computation of the entanglement asymmetry for a periodically driven conformal field theory (CFT) on a strip. Such a driven CFT, depending on the drive amplitude and frequency, exhibits two distinct phases, heating and non-heating, that are separated by a critical line. Our results show that for (m) cycles of a periodic drive with time period (T), (\Delta S \sim \ln mT) [(\ln (\ln mT))] in the heating phase [on the critical line] for a generic CFT; in contrast, in the non-heating phase, (\Delta S) displays small amplitude oscillations around it’s initial value as a function of (mT). We provide a phase diagram for the behavior of (\Delta S) for such driven CFTs as a function of the drive frequency and amplitude.