Suicide remains a public health challenge, necessitating improved detection methods to facilitate timely intervention and treatment. This systematic review evaluates the role of Artificial Intelligence (AI) and Machine Learning (ML) in assessing suicide risk through acoustic analysis of speech. Following PRISMA guidelines, we analyzed 33 articles selected from PubMed, Cochrane, Scopus, and Web of Science databases. The last search was conducted in February 2025. Risk of bias was assessed using the PROBAST tool. Studies analyzing acoustic features between individuals at risk of suicide (RS) and those not at risk (NRS) were included, while studies lacking acoustic data, a suicide-related focus, or sufficient methodological details were excluded. Sample sizes varied widely and were reported in terms of participants or speech segments, depending on the study. Results were synthesized narratively based on acoustic features and classifier performance. Findings consistently showed significant acoustic feature variations between RS and NRS populations, particularly involving jitter, fundamental frequency (F0), Mel-frequency cepstral coefficients (MFCC), and power spectral density (PSD). Classifier performance varied based on algorithms, modalities, and speech elicitation methods, with multimodal approaches integrating acoustic, linguistic, and metadata features demonstrating superior performance. Among the 29 classifier-based studies, reported AUC values ranged from 0.62 to 0.985 and accuracies from 60% to 99.85%. Most datasets were imbalanced in favor of NRS, and performance metrics were rarely reported separately by group, limiting clear identification of direction of effect.