Electroweak radiative corrections to the cross section of the process $e^+ e^- to Z H$ are considered. The complete one-loop electroweak radiative corrections are evaluated with the help of the SANC system. Higher-order contributions of the initial state radiation are computed in the QED structure function formalism. Numerical results are produced by a new version of the ReneSANCe event generator and MCSANCee integrator for the conditions of future electron-positron colliders. The resulting theoretical uncertainty in the description of this process is estimated.