Autism spectrum disorder (ASD) is characterized by difficulties in social communication and interaction, which have been related to atypical neural processing of rewards, especially in the social domain. Since intranasal oxytocin has been shown to modulate activation of the brain’s reward circuit, oxytocin could be a useful tool to ameliorate the processing of social rewards in ASD and thus improve social difficulties. In this randomized, double-blind, placebo-controlled, crossover fMRI study, we examined effects of a 24 IU dose of intranasal oxytocin on reward-related brain function in 37 men with an ASD diagnosis and 37 age- and IQ-matched control participants. Participants performed an incentive delay task that allows the investigation of neural activity associated with the anticipation and receipt of monetary and social rewards. Apart from a specific interaction effect in a single voxel within the left amygdala during the receipt of rewards, oxytocin did not influence neural processes related to the anticipation or consumption of social or monetary rewards in either group. Exploratory analyses suggested that oxytocin may increase ventral striatum sensitivity to monetary, but not social rewards, in individuals with high levels of self-reported anxiety, depression, alexithymia, and autistic traits irrespective of an ASD diagnosis. There were no significant differences in reward-related brain function between the two groups under placebo. Overall, our results do not support the hypothesis that intranasal oxytocin generally enhances activation of reward-related neural circuits in men with and without ASD without intellectual impairment. How and if oxytocin can be beneficial in the treatment of social difficulties in ASD needs to be addressed by examining moderating influences of individual differences and context on reward-related oxytocin effects.