(1) Background: Head and Neck Squamous Cell Carcinoma (HNSCC) is one of the most common malignancies globally. An early diagnosis of this disease is crucial, and the detection of gene mutations in circulating tumour DNA (ctDNA) through a liquid biopsy is a promising non-invasive diagnostic method. This review aims to provide an overview of ctDNA mutations in HNSCC patients and discuss the potential use of this tool in diagnosis and prognosis. (2) Methods: A systematic search for articles published in the English language between January 2000 and April 2021 in the Medline and Scopus databases was conducted. (3) Results: A total of 10 studies published in nine publications were selected and analysed. Altogether, 390 samples were obtained from HNSCC patients, and 79 control samples were evaluated. The most often explored gene mutation in ctDNA was TP53. (4) Conclusions: The examination of a larger group of gene mutations and the use of a combination of multiple detection methods contribute to a higher detection rate of mutated ctDNA. More studies are necessary to verify these conclusions and to translate them into clinical practice.