Nature-based solutions represent a decentralized wastewater treatment proposal, offering diverse mechanisms for effectively removing emerging contaminants, particularly acidic pharmaceuticals. This study evaluated the performance of acidic-drug (diclofenac, fenofibrate, ibuprofen, gemfibrozil, fenoprofen, naproxen, and indomethacin) removal from wastewater using a surface-flow constructed wetland with an organic bed (Eichhornia crassipes (Mart.) Solms, 18 ind/m2), and a horizontal subsurface-flow constructed wetland, divided into three sections. The process was complemented by two stabilization ponds and other horizontal subsurface-flow wetlands using papyrus (Cyperus papyrus L., 8–13 ind/m2) and tezontle as support media. The industrial-scale system (67.8 m2) was fed with wastewater at a rate of 1.33 m3/d with a hydraulic time retention of about 5.8 days. Drugs were quantified by gas chromatography. The results showed that gemfibrozil and indomethacin were completely removed (100%), while diclofenac (73%) and naproxen (94%) showed significant removals. Fenoprofen was not removed. Ibuprofen and fenofibrate showed increased concentrations, resulting in negative removals due to anoxic conditions (ibuprofen) and a slightly neutral pH (fenofibrate). These findings underscore the system’s ability to improve water quality by removing most acidic drugs, suggesting that the hybrid design is particularly effective in treating specific wastewater contaminants.