In the human speech signal, cues of speech sounds and voice identities are conflated, but they are processed separately in the human brain. The processing of speech sounds and voice identities is typically performed by non-primary auditory regions in humans and non-human primates. Additionally, these processes exhibit functional asymmetry in humans, indicating the involvement of distinct mechanisms. Behavioural studies indicate analogue side biases in dogs, but neural evidence for this functional dissociation is missing. In two experiments, using an fMRI adaptation paradigm, we presented awake dogs with natural human speech that either varied in segmental (change in speech sound) or suprasegmental (change in voice identity) content. In auditory regions, we found a repetition enhancement effect for voice identity processing in a secondary auditory region - the caudal ectosylvian gyrus. The same region did not show repetition effects for speech sounds, nor did the primary auditory cortex exhibit sensitivity to changes either in the segmental or in the suprasegmental content. Furthermore, we did not find evidence for functional asymmetry neither in the processing of speech sounds or voice identities. Our results in dogs corroborate former human and non-human primate evidence on the role of secondary auditory regions in the processing of suprasegmental cues, suggesting similar neural sensitivity to the identity of the vocalizer across the mammalian order.