A domain-specific perspective to cognitive functioning in stroke patients may predict their cognitive recovery over time and target stroke rehabilitation intervention. However, data about domain-specific cognitive impairment after stroke are still scarce. This study prospectively investigated the domain-specific pattern of cognitive impairments, using the classification proposed by the Montreal Cognitive Assessment (MoCA), in a cohort of 49 stroke patients at admission (T0), discharge (T1), and six-month follow-up (T2) from subacute intensive rehabilitation. The predictive value of T0 cognitive domains cognitive impairment at T1 and T2 was also investigated. Patients’ cognitive functioning at T0, T1, and T2 was assessed through the MoCA domains for executive functioning, attention, language, visuospatial, orientation, and memory. Different evolutionary trends of cognitive domain impairments emerged across time-points. Patients’ impairments in all domains decreased from T0 to T1. Attention and executive impairments decreased from T0 to T2 (42.9% and 26.5% to 10.2% and 18.4%, respectively). Conversely, altered visuospatial, language, and orientation increased between T1 and T2 (16.3%, 36.7%, and 40.8%, respectively). Additionally, patients’ global cognitive functioning at T1 was predicted by the language and executive domains in a subacute phase (p = 0.031 and p = 0.001, respectively), while in the long term, only attention (p = 0.043) and executive (p = 0.019) domains intervened. Overall, these results confirm the importance of a domain-specific approach to target cognitive recovery across time in stroke patients.