Inhibition modulates receptive field properties and integrative responses of neurons in cortical circuits. The contribution of specific interneuron classes to cortical circuits and emergent responses is unknown. Here, we examined neuronal responses in primary visual cortex (V1) of adult Dlx1(-/-) mice, which have a selective reduction in cortical dendrite-targeting interneurons (DTIs) that express calretinin, neuropeptide Y, and somatostatin. The V1 neurons examined in Dlx1(-/-) mice have reduced orientation selectivity and altered firing rates, with elevated late responses, suggesting that local inhibition at dendrites has a specific role in modulating neuronal computations. We did not detect overt changes in the physiological properties of thalamic relay neurons and features of thalamocortical projections, such as retinotopic maps and eye-specific inputs, in the mutant mice, suggesting that the defects are cortical in origin. These experimental results are well explained by a computational model that integrates broad tuning from dendrite-targeting and narrower tuning from soma-targeting interneuron subclasses. Our findings suggest a key role for DTIs in the fine-tuning of stimulus-specific cortical responses.