Overexpression of ferritin heavy chain (FTH1) often associates with good prognosis in breast cancer (BCa), particularly in the triple‐negative subtype (triple‐negative breast cancer). However, the mechanism by which FTH1 exerts its possible tumor suppressor effects in BCa is not known. Here, we examined the bearing of FTH1 silencing or overexpression on several aspects of BCa cell growth in vitro. FTH1 silencing promoted cell growth and mammosphere formation, increased c‐MYC expression, and reduced cell sensitivity to chemotherapy. In contrast, FTH1 overexpression inhibited cell growth, decreased c‐MYC expression, and sensitized cancer cells to chemotherapy; silencing of c‐MYC recapitulated the effects of FTH1 overexpression. These findings show for the first time that FTH1 suppresses tumor growth by inhibiting the expression of key oncogenes, such as c‐MYC.