22q11.2 deletion syndrome (22q11DS) represents a homogeneous model of schizophrenia particularly suitable for the search of neural biomarkers of psychosis. Impairments in structural connectivity related to the presence of psychotic symptoms have been reported in patients with 22q11DS. However, the relationships between connectivity changes in patients with different symptomatic profiles are still largely unknown and warrant further investigations. In this study, we used structural connectivity to discriminate patients with 22q11DS with (N = 31) and without (N = 31) attenuated positive psychotic symptoms. Different structural connectivity measures were used, including the number of streamlines connecting pairs of brain regions, graph theoretical measures, and diffusion measures. We used univariate group comparisons as well as predictive multivariate approaches. The univariate comparison of connectivity measures between patients with or without attenuated positive psychotic symptoms did not give significant results. However, the multivariate prediction revealed that altered structural network architecture discriminates patient subtypes (accuracy = 67.7%). Among the regions contributing to the classification we found the anterior cingulate cortex, which is known to be associated to the presence of psychotic symptoms in patients with 22q11DS. Furthermore, a significant discrimination (accuracy = 64%) was obtained with fractional anisotropy and radial diffusivity in the left inferior longitudinal fasciculus and the right cingulate gyrus. Our results point to alterations in structural network architecture and white matter microstructure in patients with 22q11DS with attenuated positive symptoms, mainly involving connections of the limbic system. These alterations may therefore represent a potential biomarker for an increased risk of psychosis that should be further tested in longitudinal studies.