For successful language production in a target language, bilingual individuals with aphasia must inhibit interference from the non-target language. It is currently unknown if successful inhibition of a non-target language involves general cognitive control (domain-general cognitive control) or whether it is control specific to linguistic mechanisms (domain-specific language control) during language production. The primary aim of this systematic quantitative literature review was to identify and synthesize available evidence, in relation to bilinguals with aphasia, for these two mechanisms. We conducted a literature search across five databases using a set of inclusion/exclusion criteria designed for the review. We extracted data from twenty studies reporting original research in bilinguals with aphasia. The results provided evidence for both domain-general cognitive control and domain-specific language control mechanisms, although most studies showed the involvement of domain-general cognitive control. Available neuroimaging data indicated that the neural regions involved in domain-general language control in bilinguals with aphasia were the anterior cingulate cortex, caudate nucleus, basal ganglia, and the frontal lobe. Theoretical implications for the bilingual inhibitory control model, clinical implications for assessment and treatment of cognitive control abilities in bilinguals with aphasia as well the need for future research are discussed.