Hazelnut shells, a by-product of the kernel industry processing, are reported to contain high amount of polyphenols. However, studies on the chemical composition and potential effects on human health are lacking. A methanol hazelnut shells extract was prepared and dried. Our investigation allowed the isolation and characterization of different classes of phenolic compounds, including neolignans, and a diarylheptanoid, which contribute to a high total polyphenol content (193.8 ± 3.6 mg of gallic acid equivalents (GAE)/g of extract). Neolignans, lawsonicin and cedrusin, a cyclic diarylheptanoid, carpinontriol B, and two phenol derivatives, C-veratroylglycol, and β-hydroxypropiovanillone, were the main components of the extract (0.71%–2.93%, w/w). The biological assays suggested that the extract could be useful as a functional ingredient in food technology and pharmaceutical industry showing an in vitro scavenging activity against the radical 1,1-diphenyl-2-picrylhydrazyl radical (DPPH) (EC50 = 31.7 μg/mL with respect to α-tocopherol EC50 = 10.1 μg/mL), and an inhibitory effect on the growth of human cancer cell lines A375, SK-Mel-28 and HeLa (IC50 = 584, 459, and 526 μg/mL, respectively). The expression of cleaved forms of caspase-3 and poly(ADP-ribose) polymerase-1 (PARP-1) suggested that the extract induced apoptosis through caspase-3 activation in both human malignant melanoma (SK-Mel-28) and human cervical cancer (HeLa) cell lines. The cytotoxic activity relies on the presence of the neolignans (balanophonin), and phenol derivatives (gallic acid), showing a pro-apoptotic effect on the tested cell lines, and the neolignan, cedrusin, with a cytotoxic effect on A375 and HeLa cells.