Piezoelectric actuation represents the most effective out-of-plane actuation mechanism for resonant microstructures as scanning micromirrors and piezoelectric ultrasonic transducers. Nevertheless, predicting the dynamic response of such devices at their design stage is often impractical since numerical computation of periodic orbits from finite element systems is computational demanding. In this work, we propose a model order reduction strategy based on the direct parametrisation for invariant manifolds tailored for nonlinear piezoelectric structures. The innovative aspect of the method is the introduction of nonlinear terms that arise due to piezoelectric coupling in the reduction procedure.