Allostatic load (AL) is a multisystemic indicator of the cumulative “wear and tear” on the body caused by chronic stress. In oncology, high AL is associated with a poorer prognosis, a higher number of postoperative complications, and lower treatment tolerance. Patients with head and neck cancer (HNC)—due to frequent smoking, alcohol abuse, low socioeconomic status, and high psychological and functional burden—belong to a group particularly vulnerable to high AL; however, its role in this population remains poorly understood. This narrative review includes publications from 2015 to 2026 from the PubMed/MEDLINE, Embase, and Scopus databases. We analyzed original studies, systematic reviews, and narrative reviews concerning AL in oncology, prehabilitation, and HNC. Additionally, we employed the snowballing method and included studies from key research groups. The results reveal a clear research gap—the lack of direct studies evaluating AL in HNC patients. In other cancers (breast, colorectal, lung), high AL is an independent risk factor for complications, longer hospital stays, and poorer survival. Multimodal prehabilitation (exercise, nutritional, and psychological support) shows potential for reducing AL, but no prospective studies evaluating this effect have been conducted in the HNC population. Assessment of AL may serve as a valuable tool for preoperative risk stratification and monitoring the effects of prehabilitation in patients with head and neck cancer. Prospective cohort and randomized trials are needed to integrate AL into precision medicine for this patient group.