Understanding the nonequilibrium dynamics of many-body quantum systems is typically a very hard task, due the exponential increase of the Hilbert space dimension with the number of the system’s components. Though, in the case of quantum integrable models, a large-scale description of the nonequilibrium dynamics is attained by means of an Euler hydrodynamic theory characterized by the presence of infinitely many conservation laws, dubbed Generalized Hydrodynamics (GHD). However, although GHD is able to predict the outcome of some experimental measures with great accuracy, such hydrodynamic viewpoint on the dynamics leads to a loss of large-scale quantum fluctuations and, consequently, to vanishing equal-time correlations. In order to capture these missing quantum effects, we incorporate an effective field theory description of leading quantum fluctuations over the evolving semi-classical background established by GHD. The resulting theory, called Quantum Generalized Hydrodynamics, gives asymptotically exact results for the dynamics of entanglement and of equal-time correlations which are not accessible by other standard methods at the current state of the art.