We study theoretically quantum dynamics of interacting bosons in artificial magnetic fields as engineered in recent ultracold atomic experiments, where quantum cyclotron orbital motion has been observed. With exact numerical simulations and perturbative analyses, we find that interactions induce damping in the cyclotron motion. The damping time is found to be dependent on interaction and tunneling strengths monotonically, while its dependence on magnetic flux is nonmonotonic. Sufficiently strong interactions would render bosons dynamically localized, inhibiting the cyclotron motion. The damping predicted by us can be construed as an interaction-induced quantum decoherence of the cyclotron motion.