Childhood apraxia of speech (CAS) is a subtype of motor speech disorder usually co-occurring with language impairment. A supramodal processing difficulty, involving executive functions (EFs), might contribute to the cognitive endophenotypes and behavioral manifestations. The present study aimed to profile the EFs in CAS, investigating the relationship between EFs, speech and language severity, and the connectivity of the frontal aslant tract (FAT), a white matter tract involved in both speech and EFs. A total of 30 preschool children with CAS underwent speech, language, and EF assessments and brain MRIs. Their FAT connectivity metrics were compared to those of 30 children without other neurodevelopmental disorders (NoNDs), who also underwent brain MRIs. Alterations in some basic EF components were found. Inhibition and working memory correlated with speech and language severity. Compared to NoND children, a weak, significant reduction in fractional anisotropy (FA) in the left presupplementary motor area (preSMA) FAT component was found. Only speech severity correlated and predicted FA values along with the FAT in both of its components, and visual-spatial working memory moderated the relationship between speech severity and FA in the left SMA. Our study supports the conceptualization of a composite and complex picture of CAS, not limited to the speech core deficit, but also involving high-order cognitive skills.