Background: Voice assistants allow users to control appliances and functions of a smart home by simply uttering a few words. Such systems hold the potential to significantly help users with motor and cognitive disabilities who currently depend on their caregiver even for basic needs (eg, opening a door). The research on voice assistants is mainly dedicated to able-bodied users, and studies evaluating the accessibility of such systems are still sparse and fail to account for the participants’ actual motor, linguistic, and cognitive abilities. Objective: The aim of this work is to investigate whether cognitive and/or linguistic functions could predict user performance in operating an off-the-shelf voice assistant (Google Home). Methods: A group of users with disabilities (n=16) was invited to a living laboratory and asked to interact with the system. Besides collecting data on their performance and experience with the system, their cognitive and linguistic skills were assessed using standardized inventories. The identification of predictors (cognitive and/or linguistic) capable of accounting for an efficient interaction with the voice assistant was investigated by performing multiple linear regression models. The best model was identified by adopting a selection strategy based on the Akaike information criterion (AIC). Results: For users with disabilities, the effectiveness of interacting with a voice assistant is predicted by the Mini-Mental State Examination (MMSE) and the Robertson Dysarthria Profile (specifically, the ability to repeat sentences), as the best model shows (AIC=130.11). Conclusions: Users with motor, linguistic, and cognitive impairments can effectively interact with voice assistants, given specific levels of residual cognitive and linguistic skills. More specifically, our paper advances practical indicators to predict the level of accessibility of speech-based interactive systems. Finally, accessibility design guidelines are introduced based on the performance results observed in users with disabilities.