The increasing number of skin cancer cases worldwide and the adverse side effects of current treatments have led to the search for new anticancer agents. In this present work, the anticancer potential of the natural flavanone 1, extracted fromEysenhardtia platycarpa, and four flavanone derivatives 1a–d obtained by different reactions from 1 was investigated by an in silico study and through cytotoxicity assays in melanoma (M21), cervical cancer (HeLa) cell lines and in a non-tumor cell line (HEK-293). The free compounds and compounds loaded in biopolymeric nanoparticles (PLGA NPs 1, 1a–d) were assayed. A structure–activity study (SAR) was performed to establish the main physicochemical characteristics that most contribute to cytotoxicity. Finally, ex vivo permeation studies were performed to assess the suitability of the flavanones for topical administration. Results revealed that most of the studied flavanones and their respective PLGA NPs inhibited cell growth depending on the concentration; 1b should be highlighted. The descriptors of the energetic factor were those that played a more important role in cellular activity. PLGA NPs demonstrated their ability to penetrate (Qpof 17.84−118.29 µg) and be retained (Qrof 0.01−1.44 g/gskin/cm2) in the skin and to exert their action for longer. The results of the study suggest that flavanones could offer many opportunities as a future anticancer topical adjuvant treatment.