When auditory neurons are stimulated with a pair of sounds, the preceding sound can inhibit the neural responses to the succeeding sound. This phenomenon, referred to as ‘forward suppression’, has been linked to perceptual forward masking. Previous studies investigating forward suppression typically measured the interaction between masker and probe sounds using a fixed sound location. However, in natural environments, interacting sounds often come from different spatial locations. The present study investigated two questions regarding forward suppression in the primary auditory cortex and adjacent caudal field of awake marmoset monkeys. First, what is the relationship between the location of a masker and its effectiveness in inhibiting neural response to a probe? Second, does varying the location of a masker change the spectral profile of forward suppression? We found that a masker can inhibit a neuron's response to a probe located at a preferred location even when the masker is located at a non‐preferred location of a neuron. This is especially so for neurons in the caudal field. Furthermore, we found that the strongest forward suppression is observed when a masker's frequency is close to the best frequency of a neuron, regardless of the location of the masker. These results reveal, for the first time, the stability of forward masking in cortical processing of multiple sounds presented from different locations. They suggest that forward suppression in the auditory cortex is spectrally specific and spatially broad with respect to the frequency and location of the masker, respectively.