We demonstrate an optical quantum nondemolition (QND) interaction gate with a bandwidth of about 100 MHz. Employing this gate, we are able to perform QND measurements in real time on randomly fluctuating signals. Our QND gate relies upon linear optics and offline-prepared squeezed states. In contrast to previous demonstrations on narrow sideband modes, our gate is compatible with non-Gaussian quantum states temporally localized in a wave-packet mode, and thus opens the way for universal gate operations and realization of quantum error correction.