Plant biodiversity is an important source of compounds with medicinal properties. The alkaloid galanthamine, first isolated from Galanthus woronowii (Amaryllidaceae), is approved by the FDA for the palliative treatment of mild to moderate Alzheimer’s disease due to its acetylcholinesterase (AChE) inhibitory activity. Obtaining this active pharmaceutical ingredient, still sourced on an industrial scale from the Amaryllidaceae species, is a challenge for pharmaceutical companies due to its low natural yield and the high cost of its synthesis. The aim of this work was to determine the alkaloid profile of three different Rauhia (Amaryllidaceae) species collected in Peru, and to assess the potential application of their extracts for the treatment of Alzheimer’s disease. The alkaloids were identified by gas chromatography coupled to mass spectrometry (GC-MS), and the AChE inhibitory activity of the extracts was analyzed. Thirty compounds were quantified from the Rauhia species, the R. multiflora extract being the most interesting due to its high diversity of galanthamine-type structures. The R. multiflora extract was also the most active against AChE, with the half maximal inhibitory concentration (IC50) values of 0.17 ± 0.02 μg·mL−1 in comparison with the IC50 values of 0.53 ± 0.12 μg·mL−1 for galanthamine, used as a reference. Computational experiments were carried out on the activity of the galanthamine-type alkaloids identified in R. multiflora toward five different human AChE structures. The simulation of the molecules 3-O-acetylgalanthamine, 3-O-acetylsanguinine, narwedine, and lycoraminone on the 4EY6 crystal structure theoretically showed a higher inhibition of hAChE and different interactions with the active site compared to galanthamine. In conclusion, the results of this first alkaloid profiling of the Rauhia species indicate that R. multiflora is an important natural source of galanthamine-type structures and could be used as a model for the development of biotechnological tools necessary to advance the sustainable production of galanthamine.