Speech carries identity-diagnostic acoustic cues that help individuals recognize each other during vocal–social interactions. In humans, fundamental frequency, formant dispersion and harmonics-to-noise ratio serve as characteristics along which speakers can be reliably separated. The ability to infer a speaker’s identity is also adaptive for members of other species (like companion animals) for whom humans (as owners) are relevant. The acoustic bases of speaker recognition in non-humans are unknown. Here, we tested whether dogs can recognize their owner’s voice and whether they rely on the same acoustic parameters for such recognition as humans use to discriminate speakers. Stimuli were pre-recorded sentences spoken by the owner and control persons, played through loudspeakers placed behind two non-transparent screens (with each screen hiding a person). We investigated the association between acoustic distance of speakers (examined along several dimensions relevant in intraspecific voice identification) and dogs’ behavior. Dogs chose their owner’s voice more often than that of control persons’, suggesting that they can identify it. Choosing success and time spent looking in the direction of the owner’s voice were positively associated, showing that looking time is an index of the ease of choice. Acoustic distance of speakers in mean fundamental frequency and jitter were positively associated with looking time, indicating that the shorter the acoustic distance between speakers with regard to these parameters, the harder the decision. So, dogs use these cues to discriminate their owner’s voice from unfamiliar voices. These findings reveal that dogs use some but probably not all acoustic parameters that humans use to identify speakers. Although dogs can detect fine changes in speech, their perceptual system may not be fully attuned to identity-diagnostic cues in the human voice.