Speech information inherent in face movements is important for understanding what is said in face-to-face communication. Individuals with autism spectrum disorders (ASD) have difficulties in extracting speech information from face movements, a process called visual-speech recognition. Currently, it is unknown what dysfunctional brain regions or networks underlie the visual-speech recognition deficit in ASD. We conducted a functional magnetic resonance imaging (fMRI) study with concurrent eye tracking to investigate visual-speech recognition in adults diagnosed with high-functioning autism and pairwise matched typically developed controls. Compared to the control group (n = 17), the ASD group (n = 17) showed decreased Blood Oxygenation Level Dependent (BOLD) response during visual-speech recognition in the right visual area 5 (V5/MT) and left temporal visual speech area (TVSA) - brain regions implicated in visual-movement perception. The right V5/MT showed positive correlation with visual-speech task performance in the ASD group, but not in the control group. Psychophysiological interaction analysis (PPI) revealed that functional connectivity between the left TVSA and the bilateral V5/MT and between the right V5/MT and the left IFG was lower in the ASD than in the control group. In contrast, responses in other speech-motor regions and their connectivity were on the neurotypical level. Reduced responses and network connectivity of the visual-movement regions in conjunction with intact speech-related mechanisms indicate that perceptual mechanisms might be at the core of the visual-speech recognition deficit in ASD. Communication deficits in ASD might at least partly stem from atypical sensory processing and not higher-order cognitive processing of socially relevant information.