Oxidative stress can damage neuronal cells, greatly contributing to neurodegenerative diseases (NDs). In this study, the protective activity of arzanol, a natural prenylated α-pyrone-phloroglucinol heterodimer, was evaluated against the H2O2-induced oxidative damage in trans-retinoic acid-differentiated (neuron-like) human SH-SY5Y cells, widely used as a neuronal cell model of neurological disorders. The pre-incubation (for 2 and 24 h) with arzanol (5, 10, and 25 μM) significantly preserved differentiated SH-SY5Y cells from cytotoxicity (MTT assay) and morphological changes induced by 0.25 and 0.5 mM H2O2. Arzanol reduced the generation of reactive oxygen species (ROS) induced by 2 h oxidation with H2O2 0.5 mM, established by 2′,7′-dichlorodihydrofluorescein diacetate assay. The 2 h incubation of differentiated SH-SY5Y cells with H2O2 determined a significant increase in the number of apoptotic cells versus control cells, evaluated by propidium iodide fluorescence assay (red fluorescence) and NucView® 488 assay (green fluorescence). Arzanol pre-treatment (2 h) exerted a noteworthy significant protective effect against apoptosis. In addition, arzanol was tested, for comparison, in undifferentiated SH-SY5Y cells for cytotoxicity and its ability to protect against H2O2-induced oxidative stress. Furthermore, the PubChem database and freely accessible web tools SwissADME and pkCSM-pharmacokinetics were used to assess the physicochemical and pharmacokinetic properties of arzanol. Our results qualify arzanol as an antioxidant agent with potential neuroprotective effects against neuronal oxidative stress implicated in NDs.