The mineral composition of monovarietal red wines from the Canary Islands was analyzed to evaluate the potential of mineral content as a marker for wine authenticity by geographical origin. Key minerals—K, Na, Mg, Mn, Fe, Cu, and Co—were quantified in 190 wine samples using flame absorption spectrometry. The study revealed slight mineral profile differences between recently introduced international grape cultivars and traditional ungrafted varieties. A significant correlation was found between K and Mg, highlighting their roles in vine physiology. Results indicated that Tenerife wines had elevated Fe and Mn, Lanzarote wines showed higher Na (likely from marine aerosols), and La Gomera wines had significantly high Mn. Linear Discriminant Analysis demonstrated that Mn, Mg, and Na differentiated wines by island, with 85% classification accuracy, while Cu and Fe correlated with wine aging. These findings emphasize the influence of volcanic soils and microclimate on mineral profiles, supporting mineral analysis as a cost-effective tool for classifying red wines by origin. This study offers insights into how terroir, grape cultivar, and winemaking practices define the unique characteristics of Canary Island wines.