  We study the combined effect of quasiperiodic disorder, driven and
interaction in the periodically kicked Aubry-Andr\'{e} model. In the
non-interacting limit, by analyzing the quasienergy spectrum statistics, we
verify the existence of a dynamical localization transition in the
high-frequency region, whereas the spectrum statistics becomes intricate in the
low-frequency region due to the emergence of the
extended/localized-to-multifractal edges in the quasienergy spectrum, which
separate the multifractal states from the extended (localized) states. When the
interaction is introduced, we find the periodically kicked incommensurate
potential can lead to a transition from ergodic to many-body-localization phase
in the high-frequency region. However, the many-body localization phase
vanishes in the low-frequency region even for strong quasiperiodic disorder.
Our studies demonstrate that the periodically kicked Aubry-Andr\'{e} model
displays rich dynamical phenomena and the driving frequency plays an important
role in the formation of many-body localization in addition to the disorder
strength.
