||We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the data. By testing our method with an exactly calculable model and applying it to practical dynamical mean-field calculations, we find that intermediate-frequency behaviors of Green's functions are determined solely by causality, and noncausal statistical errors are removed very efficiently. Furthermore, we demonstrate that numerical calculations of the physical branch of the Luttinger-Ward functional can be stabilized by ensuring causality of the noninteracting Green's function. Our method and findings provide a basis for improving stability and efficiency of numerical simulations of quantum many-body systems.