Suicide is a pressing public health issue, with over 700,000 individuals dying each year. Ketamine has emerged as a promising treatment for suicidal thoughts and behaviors (STBs), yet the complex mechanisms underlying ketamine’s anti-suicidal effect are not fully understood. Computational psychiatry provides a promising framework for exploring the dynamic interactions underlying suicidality and ketamine’s therapeutic action, offering insight into potential biomarkers, treatment targets, and the underlying mechanisms of both. This paper provides an overview of current computational theories of suicidality and ketamine’s mechanism of action, and discusses various computational modeling approaches that attempt to explain ketamine’s anti-suicidal effect. More specifically, the therapeutic potential of ketamine is explored in the context of the mismatch negativity and the predictive coding framework, by considering neurocircuits involved in learning and decision-making, and investigating altered connectivity strengths and receptor densities targeted by ketamine. Theory-driven computational models offer a promising approach to integrate existing knowledge of suicidality and ketamine, and for the extraction of model-derived mechanistic parameters that can be used to identify patient subgroups and personalized treatment approaches. Future computational studies on ketamine’s mechanism of action should optimize task design and modeling approaches to ensure parameter reliability, and external factors such as set and setting, as well as psychedelic-assisted therapy should be evaluated for their additional therapeutic value.