Semaglutide, a glucagon-like peptide-1 receptor agonist (GLP-1RA) marketed as Ozempic and Wegovy, is now among the most widely prescribed medications for type 2 diabetes and obesity. Rodent carcinogenicity studies demonstrated dose- and duration-dependent thyroid C-cell tumors, prompting a boxed warning for medullary thyroid carcinoma (MTC) and multiple endocrine neoplasia type 2 (MEN2), but whether this concern extends to papillary thyroid carcinoma (PTC), a follicular-cell-derived malignancy with distinct biology, remains uncertain. This narrative review evaluates current evidence on semaglutide and PTC, examining incidence, progression in patients with existing disease, receptor expression and mechanistic data, pharmacovigilance signals, sex-based patterns, and case reports published through August 2026. A pooled analysis of 93 trials (101,732 participants) and several national cohort studies found no statistically significant increase in thyroid cancer risk, and a matched cohort of 1072 patients with existing differentiated thyroid cancer found no association between GLP-1RA exposure and structural progression over a median of 69 months. A French case-control study and two FAERS disproportionality analyses reported elevated risk signals subject to detection bias and confounding by obesity. Receptor expression and functional studies were inconsistent but did not generally support a proliferative effect of GLP-1R agonism on PTC cells. Taken together, current evidence does not support semaglutide as a driver of PTC incidence or progression, though this remains an area warranting further prospective, subtype-specific study.