An ultra-low-voltage microring resonator enhanced Mach-Zehnder modulator (MRR-MZM) operated at 4.2 K is proposed and theoretically investigated for the realization of high-speed optical interconnection for the Josephson-complementary metal oxide semiconductor hybrid systems. We discussed the design of the multiple InGaAs/InAlAs coupled quantum well (CQW) for the operating temperature of 4.2 K, and the structure which is expected to exhibit a significantly large change in refractive index is proposed. In addition, the MRR-MZM with the multiple CQW in the core layer is designed and its modulation characteristics are discussed. The driving voltage as low as sub mV with the modulation frequency as high as several GHz can be realized using the MRR-MZM. The proposed modulator is a highly promising candidate for an optical transmitter in optical interconnection for superconducting integrated circuits systems.