Alzheimer’s disease is characterised by a decrease in acetylcholine (ACh) levels in the brain due to the activity of acetylcholinesterase (AChE) and butyrylcholinesterase (BChE). As a result, disorders in cholinergic transmission are observed, leading to cognitive impairment. In this work, the inhibition of AChE and BChE activities by red wines made of various grape varieties was determined for the first time. There was no significant difference in the polyphenol content between the grape varieties; nevertheless, there were significant differences in the content of gentisic acid and salicylic acid, and in the inhibition of AChE and BChE between the wine samples. A statistically significant correlation between AChE inhibitory activity and salicylic acid, as well as between BChE inhibitory activity and total phenolic content, was recorded. In model solution studies, it was shown that salicylic acid effectively inhibited BChE activity at concentrations similar to the maximum concentrations found in the test wines. Hierarchical cluster analysis (HCA) revealed that the wines could be divided into three groups. Cabernet Sauvignon and Syrah wines had the highest content of salicylic acid and AChE inhibitory activity, as well as low BChE inhibitory activity. Pinot noir, Tempranillo, Regent and Rondo wines showed the lowest content of salicylic acid and low AChE inhibitory activity. Garnacha tinta, Merlot, Montepulciano and Negroamaro wines had a medium content of salicylic acid, and the highest or medium BChE inhibitory activity. This work is important for both the wine industry and for health protection.