Autism spectrum disorder (ASD) is a class of neurodevelopmental disorders characterized by persistent deficits in social communication/interaction, together with restricted/repetitive patterns of behavior. ASD is among the most heritable neuropsychiatric conditions, and while available evidence points to a complex set of genetic factors, the SHANK gene family has emerged as one of the most promising candidates. Here, we assessed ASD-related phenotypes with particular emphasis on social behavior and cognition in Shank1 mouse mutants in comparison to heterozygous and wildtype littermate controls across development in both sexes. While social approach behavior was evident in all experimental conditions and social recognition was only mildly affected by genotype, Shank1-/- null mutant mice were severely impaired in object recognition memory. This effect was particularly prominent in juveniles, not due to impairments in object discrimination, and replicated in independent mouse cohorts. At the neurobiological level, object recognition deficits were paralleled by increased brain-derived neurotrophic factor (BDNF) protein expression in the hippocampus of Shank1-/- mice; yet BDNF levels did not differ under baseline conditions. We therefore investigated changes in the epigenetic regulation of hippocampal BDNF expression and detected an enrichment of histone H3 acetylation at the Bdnf promoter1 in Shank1-/- mice, consistent with increased learning-associated BDNF. Together, our findings indicate that Shank1 deletions lead to an aberrant cognitive phenotype characterized by severe impairments in object recognition memory and increased hippocampal BDNF levels, possibly due to epigenetic modifications. This result supports the link between ASD and intellectual disability, and suggests epigenetic regulation as a potential therapeutic target.