We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding calculations based on an orbital space separation of the fragment and environment degrees of freedom. We show its potential by presenting a specific implementation of periodic range-separated DFT coupled to a quantum circuit ansatz, whereby the variational quantum eigensolver and the quantum equation-of-motion approach are used to obtain the low-lying spectrum of the embedded fragment Hamiltonian. Application of this scheme to study strongly correlated molecular systems and localized electronic states in materials is showcased through the accurate prediction of the optical properties for the neutral oxygen vacancy in magnesium oxide (MgO). Despite some discrepancies in absorption predictions, the method demonstrates competitive performance with state-of-the-art ab initio approaches, particularly evidenced by the accurate prediction of the photoluminescence emission peak.