The response of cortical neurons to a sensory stimulus is modulated by the context. In the visual cortex, for example, stimulation of a pyramidal cell's receptive-field surround can attenuate the cell's response to a stimulus in the centre of its receptive field, a phenomenon called surround suppression. Whether cortical circuits contribute to surround suppression or whether the phenomenon is entirely relayed from earlier stages of visual processing is debated. Here we show that, in contrast to pyramidal cells, the response of somatostatin-expressing inhibitory neurons (SOMs) in the superficial layers of the mouse visual cortex increases with stimulation of the receptive-field surround. This difference results from the preferential excitation of SOMs by horizontal cortical axons. By perturbing the activity of SOMs, we show that these neurons contribute to pyramidal cells' surround suppression. These results establish a cortical circuit for surround suppression and attribute a particular function to a genetically defined type of inhibitory neuron.