Over the last few years, exoskeletons have been demonstrated to be useful tools for supporting the execution of neuromotor rehabilitation sessions. However, they are still not very present in hospitals. Therapists tend to be wary of this type of technology, thus reducing its acceptability and, therefore, its everyday use in clinical practice. The work presented in this paper investigates a novel point of view that is different from that of patients, which is normally what is considered for similar analyses. Through the realization of a technology acceptance model, we investigate the factors that influence the acceptability level of exoskeletons for rehabilitation of the upper limbs from therapists’ perspectives. We analyzed the data collected from a pool of 55 physiotherapists and physiatrists through the distribution of a questionnaire. Pearson’s correlation and multiple linear regression were used for the analysis. The relations between the variables of interest were also investigated depending on participants’ age and experience with technology. The model built from these data demonstrated that the perceived usefulness of a robotic system, in terms of time and effort savings, was the first factor influencing therapists’ willingness to use it. Physiotherapists’ perception of the importance of interacting with an exoskeleton when carrying out an enhanced therapy session increased if survey participants already had experience with this type of rehabilitation technology, while their distrust and the consideration of others’ opinions decreased. The conclusions drawn from our analyses show that we need to invest in making this technology better known to the public—in terms of education and training—if we aim to make exoskeletons genuinely accepted and usable by therapists. In addition, integrating exoskeletons with multi-sensor feedback systems would help provide comprehensive information about the patients’ condition and progress. This can help overcome the gap that a robot creates between a therapist and the patient’s human body, reducing the fear that specialists have of this technology, and this can demonstrate exoskeletons’ utility, thus increasing their perceived level of usefulness.