In response to the COVID-19 pandemic, many governments around the world now recommend, or require, their citizens to cover the lower half of their face in public. Consequently, many people now wear surgical face masks in public. We investigated whether surgical face masks affected the performance of human observers, and a state-of-the-art face recognition system, on tasks of perceptual face matching. Participants judged whether two simultaneously presented face photographs showed the same person or two different people. We superimposed images of surgical masks over the faces, creating three different mask conditions: control (no masks), mixed (one face wearing a mask), and masked (both faces wearing masks). We find that surgical face masks have a large detrimental effect on human face matching performance, and that the degree of impairment is the same regardless of whether one or both faces in each pair are masked. Surprisingly, this impairment is similar in size for both familiar and unfamiliar faces. When matching masked faces, human observers are biased to reject unfamiliar faces as mismatches and to accept familiar faces as matches. Finally, the face recognition system showed very high classification accuracy for control and masked stimuli, even though it had not been trained to recognise masked faces. However, accuracy fell markedly when one face was masked and the other was not. Our findings demonstrate that surgical face masks impair the ability of humans, and naïve face recognition systems, to perform perceptual face matching tasks. Matching decisions for masked faces should be treated with caution.