Leonurus sibiricus L. has been used as a traditional and medicinal herb for many years in Asia and Europe. This species is known to have antibacterial, anti-inflammatory, and antioxidant activity and has demonstrated a reduction of intracellular reactive oxygen species. All tested extracts of L. sibiricus showed protective and DNA repair stimulating effects in Chinese hamster ovary (CHO) cells exposed to H2O2. Preincubation of the CHO cells with 0.5 mg/mL of plant extracts showed increased expression level of antioxidant genes (SOD2, CAT, and GPx). LC-MS/MS and HPLC analyses revealed the presence of nine phenolic compounds in L. sibiricus plant extracts: catechin, verbascoside, two flavonoids (quercetin and rutin), and five phenolic acids (4-hydroxybenzoic acid, chlorogenic acid, caffeic acid, p-coumaric acid, and ferulic acid). The roots and aerial parts of in vitro L. sibiricus plant extracts, which had the strongest antioxidant properties, may be responsible for stimulating CHO cells to repair oxidatively induced DNA damage, as well as protecting DNA via enhanced activation of the antioxidant genes (SOD2, CAT, and GPx) regulating intracellular antioxidant capacity. The content of phenolic compounds in in vitro raised plants was greater than the levels found in plants propagated from seeds.