  It is shown that, in the non-relativistic limit, causal fermion systems give
rise to an effective collapse theory. The nonlinear and stochastic correction
terms to the Schr\"odinger equation are derived from the causal action
principle. The dynamics of the statistical operator is described by a
deterministic equation of Kossakowski-Lindblad form. Moreover, the quantum
state undergoes a dynamical collapse compatible with Born's rule. The effective
model has similarities with the continuous spontaneous localization model, but
differs from it by a conservation law for the probability integral as well as a
non-locality in time on a microscopic length scale $\ell_{\min}$.
