Brain reorganization patterns associated with language recovery after stroke have long been debated. Studying mechanisms of spontaneous and treatment-induced language recovery in post-stroke aphasia requires a network-based approach given the potential for recruitment of perilesional left hemisphere language regions, homologous right hemisphere language regions, and/or spared bilateral domain-general regions. Recent hardware, software, and methodological advances in functional near-infrared spectroscopy (fNIRS) make it well-suited to examine this question. fNIRS is cost-effective with minimal contraindications, making it a robust option to monitor treatment-related brain activation changes over time. Establishing clear activation patterns in neurotypical adults during language and domain-general cognitive processes via fNIRS is an important first step. Some fNIRS studies have investigated key language processes in healthy adults, yet findings are challenging to interpret in the context of methodological limitations. This pilot study used fNIRS to capture brain activation during language and domain-general processing in neurotypicals and individuals with aphasia. These findings will serve as a reference when interpreting treatment-related changes in brain activation patterns in post-stroke aphasia in the future. Twenty-four young healthy controls, seventeen older healthy controls, and six individuals with left hemisphere stroke-induced aphasia completed two language tasks (i.e., semantic feature, picture naming) and one domain-general cognitive task (i.e., arithmetic) twice during fNIRS. The probe covered bilateral frontal, parietal, and temporal lobes and included short-separation detectors for scalp signal nuisance regression. Younger and older healthy controls activated core language regions during semantic feature processing (e.g., left inferior frontal gyrus pars opercularis) and lexical retrieval (e.g., left inferior frontal gyrus pars triangularis) and domain-general regions (e.g., bilateral middle frontal gyri) during hard versus easy arithmetic as expected. Consistent with theories of post-stroke language recovery, individuals with aphasia activated areas outside the traditional networks: left superior frontal gyrus and left supramarginal gyrus during semantic feature judgment; left superior frontal gyrus and right precentral gyrus during picture naming; and left inferior frontal gyrus pars opercularis during arithmetic processing. The preliminary findings in the stroke group highlight the utility of using fNIRS to study language and domain-general processing in aphasia.