Hierridin B (6), a methylated hydroquinone isolated from the marine picocyanobacterium Cyanobium sp. LEGE 06113, moderately inhibited the growth of colon adenocarcinoma HT-29 cells. Aiming to improve the potential antitumor activity of this natural product, the demethylated analogue, norhierridin B (10), as well as its structurally-related quinone (9), were synthesized and evaluated for their growth inhibitory effect on a panel of human tumor cell lines, including the triple-negative breast cancer (TNBC) cells MDA-MB-231, SKBR3, and MDA-MB-468. Norhierridin B (10) showed a potent growth inhibitory effect on all cancer cell lines. Moreover, the growth inhibitory effect of compound 10 on MDA-MB-231 cells was associated with cell cycle arrest and apoptosis. Norhierridin B (10) interfered with several p53 transcriptional targets, increasing p21, Bax, and MDM2, while decreasing Bcl-2 protein levels, which suggested the potential activation of a p53 pathway. Altogether, these results evidenced a great improvement of the antitumor activity of hydroquinone 10 when compared to 6 and its structurally-related quinone (9). Notably, hydroquinone 10 displayed a prominent growth inhibitory activity against TNBC cells, which are characterized by high therapeutic resistance.