Children with autism spectrum disorder (ASD) have difficulties in theory of mind (ToM) and executive function (EF), which may be linked because one domain (EF) affects the other (ToM). Group differences (ASD vs. typical development) were examined in both cognitive domains, as well as EF’s associations and regressions with ToM. Participants included 29 intellectually able preschoolers with ASD and 30 typical preschoolers, aged 3–6 years. EF tasks included planning and cognitive shifting measures. ToM tasks included predicting and explaining affective and location false-belief tasks. The novelty of this study lies in its in-depth examination of ToM explanation abilities in ASD alongside the role of verbal abilities (VIQ). Significant group differences emerged on most EF and ToM measures, in favor of typically developing children. Overall in the study group, EF-planning skills, EF-cognitive shifting and VIQ significantly contributed to the explained variance of ToM measures. Implications are discussed regarding the social-cognitive deficit in ASD.