The assessment of chronic musculoskeletal pain (CMP) is a challenge shared by several health professionals. Fragmented or incomplete assessment can cause deleterious consequences for the patient’s function. The objective of this paper was to propose a framework for clinical assessment of CMP based on the current literature and following the conceptual model of the International Classification of Functioning and Health (ICF). We propose that the ICF rationale may help to guide the processes, acting as a moderator of the clinical assessment, since it changes the perspective used to obtain and interpret findings during anamnesis and physical examination. Additionally, updated specific knowledge about pain, including that of pain domains and mechanisms, along with effective patient–clinician communication may act as a mediator of CMP assessment. We conduct the readers through the steps of the clinical assessment of CMP using both the proposed moderator and mediators and present a clinical example of application. We suggest that the proposed framework may help clinicians to implement a CMP assessment based on the biopsychosocial model using a critical and updated rationale, potentially improving assessment outcomes, i.e., clinical diagnosis.