Understanding the causal interactions in some brain tasks, such as face processing, remains a challenging and ambiguous process for researchers. In this study, we address this issue by employing a novel causal discovery method -Directed Acyclic Graphs via M-matrices for Acyclicity (DAGMA)- to investigate the causal structure of the brain's face-selective network and gain deeper insights into its mechanism. Using fMRI data of natural movie stimuli, we extract causal network of face-selective regions and analyze how frames containing faces influence this network. Specifically, our findings reveal that the presence of faces in the stimuli, causally affects the number of identified connections within the network. Additionally, our results highlight the crucial role of subcortical regions in satisfying causal sufficiency, emphasizing it's importance in causal studies of brain. This study provides a new perspective on understanding the causal architecture of the face-selective network of the brain, motivating further research on neural causality.