The human auditory system is capable of processing human speech even in situations when it has been heavily degraded, such as during noise-vocoding, when frequency domain-based cues to phonetic content are strongly reduced. This has contributed to arguments that speech processing is highly specialized and likely a de novo evolved trait in humans. Previous comparative research has demonstrated that a language competent chimpanzee was also capable of recognizing degraded speech, and therefore that the mechanisms underlying speech processing may not be uniquely human. However, to form a robust reconstruction of the evolutionary origins of speech processing, additional data from other closely related ape species is needed. Specifically, such data can help disentangle whether these capabilities evolved independently in humans and chimpanzees, or if they were inherited from our last common ancestor. Here we provide evidence of processing of highly varied (degraded and computer-generated) speech in a language competent bonobo, Kanzi. We took advantage of Kanzi’s existing proficiency with touchscreens and his ability to report his understanding of human speech through interacting with arbitrary symbols called lexigrams. Specifically, we asked Kanzi to recognise both human (natural) and computer-generated forms of 40 highly familiar words that had been degraded (noise-vocoded and sinusoidal forms) using a match-to-sample paradigm. Results suggest that—apart from noise-vocoded computer-generated speech—Kanzi recognised both natural and computer-generated voices that had been degraded, at rates significantly above chance. Kanzi performed better with all forms of natural voice speech compared to computer-generated speech. This work provides additional support for the hypothesis that the processing apparatus necessary to deal with highly variable speech, including for the first time in nonhuman animals, computer-generated speech, may be at least as old as the last common ancestor we share with bonobos and chimpanzees.