Spiny mice (Acomys cahirinus) are terrestrial mammals that evolved unique scar-free regenerative wound-healing properties. Myofibroblasts (MFs) are the major scar-forming cell type in skin. We found that following traumatic injury to ear pinnae, MFs appeared rapidly in both Acomys and mouse yet persisted only in mouse. The timing of MF loss in Acomys correlated with wound closure, blastema differentiation, and nuclear localization of the Hippo pathway target protein Yap. Experiments in vitro revealed an accelerated PP2A-dependent dephosphorylation activity that maintained nuclear Yap in Acomys dermal fibroblasts (DFs) and was not detected in mouse or human DFs. Treatment of Acomys in vivo with the nuclear Yap-TEAD inhibitor verteporfin prolonged MF persistence and converted tissue regeneration to fibrosis. Forced Yap activity prevented and rescued TGF-β1-induced human MF formation in vitro. These results suggest that Acomys evolved modifications of Yap activity and MF fate important for scar-free regenerative wound healing in vivo.