Fibrosis, which causes structural hardening and functional degeneration in various organs, is characterized by the excessive production and accumulation of connective tissue containing collagen, alpha-smooth muscle actin (α-SMA), etc. In traditional medicine, extracts of medicinal plants or herbal prescriptions have been used to treat various fibrotic diseases. The purpose of this narrative review is to discuss the antifibrotic effects of rosmarinic acid (RA) and plant extracts that contain RA, as observed in various experimental models. RA, as well as the extracts of Glechoma hederacea, Melissa officinalis, Elsholtzia ciliata, Lycopus lucidus, Ocimum basilicum, Prunella vulgaris, Salvia rosmarinus (Rosmarinus officinalis), Salvia miltiorrhiza, and Perilla frutescens, have been shown to attenuate fibrosis of the liver, kidneys, heart, lungs, and abdomen in experimental animal models. Their antifibrotic effects were associated with the attenuation of oxidative stress, inflammation, cell activation, epithelial–mesenchymal transition, and fibrogenic gene expression. RA treatment activated peroxisomal proliferator-activated receptor gamma (PPARγ), 5′ AMP-activated protein kinase (AMPK), and nuclear factor erythroid 2-related factor 2 (NRF2) while suppressing the transforming growth factor beta (TGF-β) and Wnt signaling pathways. Interestingly, most plants that are reported to contain RA and exhibit antifibrotic activity belong to the family Lamiaceae. This suggests that RA is an active ingredient for the antifibrotic effect of Lamiaceae plants and that these plants are a useful source of RA. In conclusion, accumulating scientific evidence supports the effectiveness of RA and Lamiaceae plant extracts in alleviating fibrosis and maintaining the structural architecture and normal functions of various organs under pathological conditions.