It is shown that the theory of causal fermion systems gives rise to a novel mechanism for dark matter and dark energy. This mechanism is first worked out for cubical subsets of Minkowski space with periodic boundary conditions. Then it is studied in Friedmann-Lemaitre-Roberson-Walker spacetimes. The magnitude of the effect scales like one over the lifetime of the Universe squared. In contrast to most models of dark matter and dark energy, our mechanism does not postulate any new particles. Instead, it is a result of the collective behavior of all the wave functions which form the Dirac sea, needed in order to arrange correlated initial and end quantum states of the Universe.