In the present study, we sought to examine whether face recognition problems impact the social anxiety experienced by autistic people. Many autistic people -- perhaps between 15% and 30% -- exhibit severe face recognition problems that closely resemble developmental prosopagnosia. At present, however, little is known about the psychosocial consequences of these difficulties. Autistic participants (N = 60) with varying degrees of face recognition ability completed two measures of face recognition (the original and Australian variants of the Cambridge Face Memory test), a measure of social anxiety (the Social Interaction Anxiety Scale) and a bespoke survey that enquired about individuals' experiences of face recognition and social interaction. Relative to autistic individuals with average or above-average face recognition, autistic individuals with poor face recognition described significantly higher levels of social anxiety. Moreover, more than half our participants felt that poor face recognition hampered their social interaction, while more than a third thought that poor face recognition had undermined their efforts to make friends. These initial results suggest that poor face recognition may be an important determinant of social anxiety in autism.