We investigate the nonlocality in microscopic optical potentials derived from chiral effective field theory. For this purpose we employ the Perey-Buck ansatz, which connects the energy dependence of purely local optical potentials to a Gaussian spatial nonlocality. We find that the dominant source of energy dependence in the microscopic real optical potential indeed arises from spatial nonlocalities, while the energy dependence associated with the microscopic imaginary optical potential is primarily a genuine time nonlocality. We present results for nonlocal nucleon-nucleus optical potentials for the calcium isotopic chain and study the dependence of the Woods-Saxon shape parameters on the isotopic number.