Vehicle passing-induced noise from bridge expansion joints has become a significant global environmental issue. In highway bridges, bridge expansion joints are commonly installed in concrete and steel box girders. The vibro-acoustic differences between the different installation methods require in-depth investigation. In this study, a novel vehicle-bridge expansion joint-bridge coupling system model was developed to investigate the vibration and noise radiation induced by vehicles passing single-gap bridge expansion joints (SBEJs). The model was calibrated using field measurements of SBEJs subjected to traffic loads. Subsequently, the spatial distribution of noise under different cases where the edge beams of SBEJs were installed in concrete box girders or steel box girders, respectively, was discussed, and the effect of different thicknesses of the anchored concrete on the vibro-acoustic characteristics of SBEJs in steel box girder was investigated. The research showed that the vertical vibration of the SBEJ is in the frequency range of 1200–3000 Hz, while the main frequency range of the noise generated by the vehicle passing through the SBEJ is 630–1000 Hz. When both edge beams of SBEJ are installed in steel box girders, the sound pressure level can be reduced with a maximum value of 3.5 dB, compared with those installed on concrete box girders. Moreover, increasing the thickness of the anchored concrete of the steel box girder can further reduce the vibro-acoustic response of the SBEJ induced by vehicles passing.