Autism spectrum disorders (ASDs) represent a diagnostic challenge with a still partially uncertain etiology, in which genetic and environmental factors have now been assessed. Among the hypotheses underlying the involvement of biological and environmental factors, the gut–brain axis is of particular interest in autism spectrum disorders. Several studies have highlighted the related incidence of particular gastrointestinal symptoms (GISs) in children suffering from ASDs. Probiotics have shown success in treating several gastrointestinal dysbiotic disorders; therefore, it is plausible to investigate whether they can alleviate behavioral symptoms as well. On these bases, a randomized double-blind crossover study with a placebo was conducted, evaluating the effects of a mixture of probiotics in a group of 61 subjects aged between 24 months and 16 years old with a diagnosis of ASD. Behavioral evaluation was performed through the administration of a questionnaire including a Parenting Stress Index (PSI) test and the Vineland Adaptive Behavior Scale (VABS). The Psycho-Educational Profile and the Autism Spectrum Rating Scale (ASRS) were also evaluated. Microbial composition analyses of fecal samples of the two groups was also performed. The study showed significant improvements in GISs, communication skills, maladaptive behaviors, and perceived parental stress level after the administration of probiotics. Microbiome alpha diversity was comparable between treatment arms and no significant differences were found, although beta diversity results were significantly different in the treatment group between T0 and T1 time points. Streptococcus thermophilus, Bifidobacterium longum, Limosilactobacillus fermentum, and Ligilactobacillus salivarius species were identified as some of the most discriminant taxa positively associated with T1 samples. This preliminary study corroborates the relationship between intestinal microbiota and ASD recently described in the literature.