In the last decades, glucosinolates (GLs), precursors of isothiocyanates (ITCs), have been studied mostly for their chemopreventive and chemotherapeutic properties. The aim of our research was to study the antiproliferative effect of 4-(α-L-rhamnopyranosyloxy) benzyl glucosinolate (glucomoringin; GMG) bioactivated by myrosinase enzyme to form the corresponding isothiocyanate 4-(α-L-rhamnopyranosyloxy) benzyl C (moringin) in SH-SY5Y human neuroblastoma cells. We found that moringin significantly reduced SH-SY5Y cell growth in a time and concentration-dependent (p < 0.05, 0.01, and 0.001 vs. ctrl, after treatment with 16.4 µM moringin for 24, 48, and 72 h, respectively) manner through a mechanism involving the activation of apoptotic machinery. In addition, it altered the normal progression of cells through the cell cycle, increasing the cell population in both G2 and S phases, as well as decreasing that in the G1 phase. Studying the drug mechanism of action, we found that moringin was able to increase the expression of p53, p21, and Bax at both the protein and transcriptional level. Moreover, exposure of SH-SY5Y cells to moringin significantly increased the gene expression of both caspase 3 and 9 and enhanced their cleavage, thereby initiating an intrinsic apoptotic cascade. Finally, moringin inhibited nuclear translocation of NF-κB. Our study demonstrates the ability of moringin to reduce the growth of SH-SY5Y cells and reveals its mechanism of action, suggesting its promising role as an anticancer drug.