We examined social cognition in 32 monozygotic (MZ) and 21 dizygotic (DZ) twin pairs concordant or discordant for a schizophrenia spectrum diagnosis and healthy control (HC) twin pairs (29 MZ/20 DZ). All participants were recruited through the Danish registers. Patients showed several deficits in the ability to detect sarcasm. Impairments were also observed in the unaffected MZ co-twins, indicating that social cognitive deficits could be a genetic vulnerability indicator of the disease. Worse social cognition was associated with lower intelligence and higher levels of psychopathology in patients.