Myotonic dystrophy type-1 (DM1) is a genetic multi-systemic disorder involving several organs including the brain. Despite the heterogeneity of this condition, some patients with non-congenital DM1 can present with minimal cognitive impairment on formal testing but with severe difficulties in daily-living activities including social interactions. One explanation for this paradoxical mismatch can be found in patients' dysfunctional social cognition, which can be assessed in the framework of the Theory of Mind (ToM). We hypothesize here that specific disease driven abnormalities in DM1 brains may result in ToM impairments. We recruited 20 DM1 patients who underwent the "Reading the Mind in the Eyes" and the ToM-story tests. These patients, together with 18 healthy controls, also underwent resting-state functional MRI. A composite Theory of Mind score was computed for all recruited patients and correlated with their brain functional connectivity. This analysis provided the patients' "Theory of Mind-network", which was compared, for its topological properties, with that of healthy controls. We found that DM1 patients showed deficits in both tests assessing ToM. These deficits were associated with specific patterns of abnormal connectivity between the left inferior temporal and fronto-cerebellar nodes in DM1 brains. The results confirm the previous suggestions of ToM dysfunctions in patients with DM1 and support the hypothesis that difficulties in social interactions and personal relationships are a direct consequence of brain abnormalities, and not a reaction symptom. This is relevant not only for a better pathophysiological comprehension of DM1, but also for non-pharmacological interventions to improve clinical aspects and impact on patients' success in life.