Quantum communication between remote superconducting systems is being studied intensively to increase the number of integrated superconducting qubits and to realize a distributed quantum computer. Since optical photons must be used for communication outside a dilution refrigerator, the direct conversion of microwave photons to optical photons has been widely investigated. However, the direct conversion approach suffers from added photon noise, heating due to a strong optical pump, and the requirement for large cooperativity. Instead, for quantum communication between superconducting qubits, we propose an entanglement distribution scheme using a solid-state spin quantum memory that works as an interface for both microwave and optical photons. The quantum memory enables quantum communication without significant heating inside the refrigerator, in contrast to schemes using high-power optical pumps. Moreover, introducing the quantum memory naturally makes it possible to herald entanglement and parallelization using multiple memories.