Background: Neuropathic pain (NP) in head and neck cancer (HNC) patients represents a treatment challenge. Most studies investigating drugs against NP are conducted in patients suffering with diabetic neuropathy or postherpetic neuralgia, while data are limited in cancer pain management. Additionally, regarding cancer therapy-related NP, most of the studies do not focus on HNC patients. The aim of this review is to identify the studies on systematically administered medication for NP management that included HNC patients under radiotherapy. Methods: A systematic literature search was performed, following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, in PubMed, Cochrane Library, Web of Science and ClinicalTrials.gov on 30 October 2021. The medical subject heading (MeSH) terms were (“head and neck cancer” OR “tumor”) AND “neuropathic pain” AND “medication” AND “radiotherapy.” The Cochrane Collaboration tool was used for quality assessment. Results: The search identified 432 articles. Three more articles were identified after searching the reference lists of the retrieved articles. A total of 10 articles met the eligibility inclusion criteria and were included in this review; 6 on gabapentin, 1 on pregabalin, 1 on nortriptyline, 1 on methadone, and 1 on ketamine. Statistically significant results in pain reduction compared to placebo or standard pain medication were found in the studies on pregabalin (p = 0.003), methadone (p = 0.03), ketamine (p = 0.012), and in two out of six gabapentin studies (p < 0.004). Two of the studies (both concerning gabapentin) had no comparison arm. Conclusions: Treatments including pregabalin, methadone, ketamine, and gabapentin were found to provide pain relief against HNC NP. While there is a plethora of pharmacological treatments available for the management of NP, only a few studies have been conducted regarding the pharmacological management of therapy-related NP in HNC patients. More studies should be conducted regarding the pharmacological approaches in HNC therapy-related NP so that specific treatment algorithms can be developed.