We study entanglement harvesting for matter systems such as atoms, ions or molecules whose center of mass degrees of freedom are quantum delocalized and which couple to a relativistic quantum field. We employ a generalized Unruh-deWitt detector model for the light-matter interaction, and we investigate how the coherent spreading of the quantum center of mass wave function of two delocalized detector systems impacts their ability to become entangled with one another, via their respective interaction with a quantum field. For very massive detectors with initially highly localized centers of mass, we recover the results of entanglement harvesting for pointlike Unruh-deWitt detectors with classical center of mass degrees of freedom. We find that entanglement harvesting is Gaussian suppressed in the initial center of mass delocalization of the detectors. We further find that spatial smearing profiles, which are commonly employed to model the finite size of atoms due to their atomic orbitals, are not suited to model center of mass delocalization. Finally, for coherently delocalized detectors, we compare entanglement harvesting in the vacuum to entanglement harvesting in media. We find that entanglement harvesting is significantly suppressed in media in which the wave propagation speed is much smaller than the vacuum speed of light.