We present two models of dark matter (DM) that can provide a natural explanation of the excess of $B^{+}\to K^{+}+\mathrm{invisible}$ events with respect to the Standard Model (SM) prediction for $B^{+}\to K^{+}\nu \overline{\nu }$, which has been reported by the Belle II Collaboration. Interactions between the dark and the visible sector are mediated by an axionlike particle in one case, by the kinetic mixing between a dark photon and the SM photon in the second case. Both models encompass a light fermion singlet as the DM candidate and can account for the observed DM relic abundance through, respectively, the freeze-in and the freeze-out production mechanism, while simultaneously explaining the Belle II excess.