Semantic memory encompasses knowledge about both the properties that typify concepts (e.g. robins, like all birds, have wings) as well as the properties that individuate conceptually related items (e.g. robins, in particular, have red breasts). We investigate the impact of sleep on new semantic learning using a property inference task in which both kinds of information are initially acquired equally well. Participants learned about three categories of novel objects possessing some properties that were shared among category exemplars and others that were unique to an exemplar, with exposure frequency varying across categories. In Experiment 1, memory for shared properties improved and memory for unique properties was preserved across a night of sleep, while memory for both feature types declined over a day awake. In Experiment 2, memory for shared properties improved across a nap, but only for the lower-frequency category, suggesting a prioritization of weakly learned information early in a sleep period. The increase was significantly correlated with amount of REM, but was also observed in participants who did not enter REM, suggesting involvement of both REM and NREM sleep. The results provide the first evidence that sleep improves memory for the shared structure of object categories, while simultaneously preserving object-unique information.