A diverse array of interneuron types regulates activity in the mammalian neocortex. Two of the most abundant are the fast-spiking, parvalbumin-positive (PV(+)) interneurons, which target the axosomatic region of pyramidal cells, and the somatostatin-positive (SOM(+)) interneurons, which target the dendrites. Recent work has focused on the influence of PV(+) and SOM(+) interneurons on pyramidal cells. However, the connections among PV(+) and SOM(+) interneurons are poorly understood and could play an important role in cortical circuitry, since their interactions may alter the net influence on pyramidal cell output. We used an optogenetic approach to investigate the effect of SOM(+) interneurons on pyramidal cells and PV(+) interneurons during visual stimulation in mouse primary visual cortex. We find that SOM(+) interneuron activation suppresses PV(+) cell spiking at least twice as potently as pyramidal cell spiking during visual stimulation. This differential effect of SOM(+) cell stimulation is detectable even when only two to three SOM(+) cells are activated. Importantly, the remaining responses to oriented gratings in PV(+) cells are more orientation tuned and temporally modulated, suggesting that SOM(+) activity unmasks this tuning by suppressing untuned input. Our results highlight the importance of SOM(+) inhibition of PV(+) interneurons during sensory processing. This prominent competitive inhibition between interneuron types leads to a reconfiguration of inhibition along the somatodendritic axis of pyramidal cells, and enhances the orientation selectivity of PV(+) cells.