We propose a method to probe time-dependent correlations of nontrivial observables in many-body ultracold lattice gases. The scheme uses a quantum nondemolition matter-light interface, first to map the observable of interest on the many-body system into the light and then to store coherently such information into an external system acting as a quantum memory. Correlations of the observable at two (or more) instances of time are retrieved with a single final measurement that includes the readout of the quantum memory. Such a method brings to reach the study of dynamics of many-body systems in and out of equilibrium by means of quantum memories in the field of quantum simulators.