Obesity and overweight represent a growing health problem worldwide. Genes regulating the intake and metabolism of different nutrients can positively or negatively influence the efficacy of nutritional interventions against obesity and its complications. The aim of this study was to assess changes in anthropometric and clinical parameters and the adherence to a Mediterranean diet (MedDiet) over time in relation to nutrigenetic variants in overweight or obese subjects affected by Type 2 Diabetes (T2D) or dysglycemia, who were included in a nutritional program. A total of 23 subjects were included in this study. Clinical parameters, physical activity levels, and the adherence to a MedDiet were evaluated at baseline, at 6 (T6), and at 12 months (T12) during and after a diet/lifestyle intervention. In a single blood sample from each subject, rs1984112 (A>G) and rs1761667 (G>A) in CD36; rs7950226 (G>A) in BMAL1; and rs1801260 (A>G), rs4864548 (A>G), and rs3736544 (G>A) in CLOCK were genotyped with Real-Time PCR. Significant associations were observed between CD36 rs1761667 and weight (p = 0.025), hip circumference (p = 0.042), triglycerides (p = 0.047), and HbA1c (p = 0.012) at baseline. Moreover, the genotype AA in CD36 rs1761667 was significantly associated with a lower BMI when compared to G carriers at baseline, at T6, and also at T12. In addition, subjects with the AA genotype at CD36 rs1984112 had significantly lower levels of HbA1c (p = 0.027) than the GG and AG genotypes at baseline. These results show that variants in CD36 can have an impact on anthropometric and clinical parameters in overweight or obese subjects affected by T2D or dysglycemia, and that it might influence the success of the diet/lifestyle intervention.