The Apolipoprotein E isoform E4 (ApoE4) is consistently associated with an elevated risk of developing late-onset Alzheimer's Disease (AD); however, less is known about the potential genetic modulation of the brain networks organization during prodromal stages like Mild Cognitive Impairment (MCI). To investigate this issue during this critical stage, we used a dataset with a cross-sectional sample of 253 MCI patients divided into ApoE4-positive (‛Carriers') and ApoE4-negative ('non-Carriers'). We estimated the cortical thickness (CT) from high-resolution T1-weighted structural magnetic images to calculate the correlation among anatomical regions across subjects and build the CT covariance networks (CT-Nets). The topological properties of CT-Nets were described through the graph theory approach. Specifically, our results showed a significant decrease in characteristic path length, clustering-index, local efficiency, global connectivity, modularity, and increased global efficiency for Carriers compared to non-Carriers. Overall, we found that ApoE4 in MCI shaped the topological organization of CT-Nets. Our results suggest that in the MCI stage, the ApoE4 disrupting the CT correlation between regions may be due to adaptive mechanisms to sustain the information transmission across distant brain regions to maintain the cognitive and behavioral abilities before the occurrence of the most severe symptoms.